Relevant bibliographies by topics / Random walk processses

Academic literature on the topic 'Random walk processses'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Random walk processses"

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Dorogovtsev, A. A., and I. I. Nishchenko. "Loop-erased random walks associated with Markov processes." Theory of Stochastic Processes 25(41), no. 2 (December 11, 2021): 15–24. http://dx.doi.org/10.37863/tsp-1348277559-92.

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A new class of loop-erased random walks (LERW) on a finite set, defined as functionals from a Markov chain is presented. We propose a scheme in which, in contrast to the general settings of LERW, the loop-erasure is performed on a non-markovian sequence and moreover, not all loops are erased with necessity. We start with a special example of a random walk with loops, the number of which at every moment of time does not exceed a given fixed number. Further we consider loop-erased random walks, for which loops are erased at random moments of time that are hitting times for a Markov chain. The asymptotics of the normalized length of such loop-erased walks is established. We estimate also the speed of convergence of the normalized length of the loop-erased random walk on a finite group to the Rayleigh distribution.
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ABRAMSON, JOSH, and JIM PITMAN. "Concave Majorants of Random Walks and Related Poisson Processes." Combinatorics, Probability and Computing 20, no. 5 (August 18, 2011): 651–82. http://dx.doi.org/10.1017/s0963548311000307.

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We offer a unified approach to the theory of concave majorants of random walks, by providing a path transformation for a walk of finite length that leaves the law of the walk unchanged whilst providing complete information about the concave majorant. This leads to a description of a walk of random geometric length as a Poisson point process of excursions away from its concave majorant, which is then used to find a complete description of the concave majorant of a walk of infinite length. In the case where subsets of increments may have the same arithmetic mean, we investigate three nested compositions that naturally arise from our construction of the concave majorant.
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Codling, Edward A., Michael J. Plank, and Simon Benhamou. "Random walk models in biology." Journal of The Royal Society Interface 5, no. 25 (April 15, 2008): 813–34. http://dx.doi.org/10.1098/rsif.2008.0014.

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Mathematical modelling of the movement of animals, micro-organisms and cells is of great relevance in the fields of biology, ecology and medicine. Movement models can take many different forms, but the most widely used are based on the extensions of simple random walk processes. In this review paper, our aim is twofold: to introduce the mathematics behind random walks in a straightforward manner and to explain how such models can be used to aid our understanding of biological processes. We introduce the mathematical theory behind the simple random walk and explain how this relates to Brownian motion and diffusive processes in general. We demonstrate how these simple models can be extended to include drift and waiting times or be used to calculate first passage times. We discuss biased random walks and show how hyperbolic models can be used to generate correlated random walks. We cover two main applications of the random walk model. Firstly, we review models and results relating to the movement, dispersal and population redistribution of animals and micro-organisms. This includes direct calculation of mean squared displacement, mean dispersal distance, tortuosity measures, as well as possible limitations of these model approaches. Secondly, oriented movement and chemotaxis models are reviewed. General hyperbolic models based on the linear transport equation are introduced and we show how a reinforced random walk can be used to model movement where the individual changes its environment. We discuss the applications of these models in the context of cell migration leading to blood vessel growth (angiogenesis). Finally, we discuss how the various random walk models and approaches are related and the connections that underpin many of the key processes involved.
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Montero, Miquel. "Random Walks with Invariant Loop Probabilities: Stereographic Random Walks." Entropy 23, no. 6 (June 8, 2021): 729. http://dx.doi.org/10.3390/e23060729.

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Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.
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Lindvall, Torgny, and L. C. G. Rogers. "On coupling of random walks and renewal processes." Journal of Applied Probability 33, no. 1 (March 1996): 122–26. http://dx.doi.org/10.2307/3215269.

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The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.
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Lindvall, Torgny, and L. C. G. Rogers. "On coupling of random walks and renewal processes." Journal of Applied Probability 33, no. 01 (March 1996): 122–26. http://dx.doi.org/10.1017/s0021900200103778.

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The use of Mineka coupling is extended to a case with a continuous state space: an efficient coupling of random walks S and S' in can be made such that S' — S is virtually a one-dimensional simple random walk. This insight settles a zero-two law of ergodicity. One more proof of Blackwell's renewal theorem is also presented.
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YANG, ZHIHUI. "LARGE DEVIATION ASYMPTOTICS FOR RANDOM-WALK TYPE PERTURBATIONS." Stochastics and Dynamics 07, no. 01 (March 2007): 75–89. http://dx.doi.org/10.1142/s0219493707001950.

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Symmetric random walks can be arranged to converge to a Wiener process in the area of normal deviation. However, random walks and Wiener processes have, in general, different asymptotics of the large deviation probabilities. The action functionals for random-walks and Wiener processes are compared in this paper. The correction term is calculated. Exit problem and stochastic resonance for random-walk-type perturbation are also considered and compared with the white-noise-type perturbation.
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Nicolau, João. "STATIONARY PROCESSES THAT LOOK LIKE RANDOM WALKS— THE BOUNDED RANDOM WALK PROCESS IN DISCRETE AND CONTINUOUS TIME." Econometric Theory 18, no. 1 (February 2002): 99–118. http://dx.doi.org/10.1017/s0266466602181060.

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Several economic and financial time series are bounded by an upper and lower finite limit (e.g., interest rates). It is not possible to say that these time series are random walks because random walks are limitless with probability one (as time goes to infinity). Yet, some of these time series behave just like random walks. In this paper we propose a new approach that takes into account these ideas. We propose a discrete-time and a continuous-time process (diffusion process) that generate bounded random walks. These paths are almost indistinguishable from random walks, although they are stochastically bounded by an upper and lower finite limit. We derive for both cases the ergodic conditions, and for the diffusion process we present a closed expression for the stationary distribution. This approach suggests that many time series with random walk behavior can in fact be stationarity processes.
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Argyrakis, Panos. "Information dimension in random-walk processes." Physical Review Letters 59, no. 15 (October 12, 1987): 1729–32. http://dx.doi.org/10.1103/physrevlett.59.1729.

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Muminov, M., and E. G. Samandarov. "Inequalities for Some Random Walk Processes." Theory of Probability & Its Applications 30, no. 3 (September 1986): 489–95. http://dx.doi.org/10.1137/1130061.

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Dissertations / Theses on the topic "Random walk processses"

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Jones, Elinor Mair. "Large deviations of random walks and levy processes." Thesis, University of Manchester, 2008. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.491853.

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Buckley, Stephen Philip. "Problems in random walks in random environments." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:06a12be2-b831-4c2a-87b1-f0abccfb9b8b.

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Recent years have seen progress in the analysis of the heat kernel for certain reversible random walks in random environments. In particular the work of Barlow(2004) showed that the heat kernel for the random walk on the infinite component of supercritical bond percolation behaves in a Gaussian fashion. This heat kernel control was then used to prove a quenched functional central limit theorem. Following this work several examples have been analysed with anomalous heat kernel behaviour and, in some cases, anomalous scaling limits. We begin by generalizing the first result - looking for sufficient conditions on the geometry of the environment that ensure standard heat kernel upper bounds hold. We prove that these conditions are satisfied with probability one in the case of the random walk on continuum percolation and use the heat kernel bounds to prove an invariance principle. The random walk on dynamic environment is then considered. It is proven that if the environment evolves ergodically and is, in a certain sense, geometrically d-dimensional then standard on diagonal heat kernel bounds hold. Anomalous lower bounds on the heat kernel are also proven - in particular the random conductance model is shown to be "more anomalous" in the dynamic case than the static. Finally, the reflected random walk amongst random conductances is considered. It is shown in one dimension that under the usual scaling, this walk converges to reflected Brownian motion.
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Oosthuizen, Joubert. "Random walks on graphs." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86244.

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Thesis (MSc)--Stellenbosch University, 2014.
ENGLISH ABSTRACT: We study random walks on nite graphs. The reader is introduced to general Markov chains before we move on more specifically to random walks on graphs. A random walk on a graph is just a Markov chain that is time-reversible. The main parameters we study are the hitting time, commute time and cover time. We nd novel formulas for the cover time of the subdivided star graph and broom graph before looking at the trees with extremal cover times. Lastly we look at a connection between random walks on graphs and electrical networks, where the hitting time between two vertices of a graph is expressed in terms of a weighted sum of e ective resistances. This expression in turn proves useful when we study the cover cost, a parameter related to the cover time.
AFRIKAANSE OPSOMMING: Ons bestudeer toevallige wandelings op eindige gra eke in hierdie tesis. Eers word algemene Markov kettings beskou voordat ons meer spesi ek aanbeweeg na toevallige wandelings op gra eke. 'n Toevallige wandeling is net 'n Markov ketting wat tyd herleibaar is. Die hoof paramaters wat ons bestudeer is die treftyd, pendeltyd en dektyd. Ons vind oorspronklike formules vir die dektyd van die verdeelde stergra ek sowel as die besemgra ek en kyk daarna na die twee bome met uiterste dektye. Laastens kyk ons na 'n verband tussen toevallige wandelings op gra eke en elektriese netwerke, waar die treftyd tussen twee punte op 'n gra ek uitgedruk word in terme van 'n geweegde som van e ektiewe weerstande. Hierdie uitdrukking is op sy beurt weer nuttig wanneer ons die dekkoste bestudeer, waar die dekkoste 'n paramater is wat verwant is aan die dektyd.
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Jones, Owen Dafydd. "Random walks on pre-fractals and branching processes." Thesis, University of Cambridge, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.388440.

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Boutaud, Pierre. "Branching random walk : limit cases and minimal hypothesis." Thesis, université Paris-Saclay, 2020. http://www.theses.fr/2020UPASM025.

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La marche aléatoire branchante est un système de particules sur la droite réelle où partant au temps 0 d’une particule initiale en position 0, chaque particule vivante au temps n meurt au temps n + 1 en donnant indépendemment naissance à un nombre aléatoire de particules se dispersant aléatoirement autour de la position de la particule parente. Dans un premier chapitre introductif, nous définissons en détails le modèle de la marche aléatoire branchante ainsi que certains des enjeux de la recherche autour de ce modèle, notamment l’étude de la martingale additive. Cette martingale peut-être étudié au travers de sa convergence vers une limite triviale ou non ainsi que l’étude d’une renormalisation appropriée, dite de Seneta-Heyde, lorsque cette limite est triviale. Elle peut aussi être étudiée au travers d’équations récursives stochastiques menant à des équations de points fixes en loi. Cette dernière question correspond à des travaux non-publiés effectués en première année de thèse en continuité avec ceux effectués en mémoire de master. Le second chapitre est une traduction en anglais de certaines sections du précédent chapitre pour faciliter la compréhension de certains lecteurs sur les points importants de cette thèse.Dans un troisième chapitre nous présentons une nouvelle méthode de preuve développée avec Pascal Maillard pour le théorème d’Aïdékon et Shi sur la renormalisation de Seneta-Heyde de la martingale additive critique dans le cas où la marche de l’épine admet une variance finie. Cette nouvelle preuve se passe du recours à un lemme d’épluchage et à des calculs de seconds moments pour lui préférer une étude de la transformée de Laplace conditionnée. Les propriétés des fonctions de renouvellements permettent une approche plus générale qui ne demande pas de s’attarder en particulier sur la martingale dérivée. Ceci est d’ailleurs illustré dans le quatrième chapitre où dans de nou veaux travaux avec Pascal Maillard, nous trouvons la renormalisation de Seneta-Heyde de la martingale additive critique dans le cas où la marche de l’épine est dans le domaine d’attraction d’une loi stable. On voit alors que les fonctions de renouvellement nous fournissent un candidat mieux adapté à cette étude que la martingale dérivée, qui n’est plus toujours une martingale dans ce nouveau contexte.Enfin, le cinquième chapitre étudie la question de l’optimalité des hypothèses faites dans le chapitre précédent quant à la trivialité ou non de la limite obtenue après renormalisation de Seneta-Heyde
The branching random walk is a particle system on the real line starting at time 0 with an initial particle at position 0, then each particle living at time n proceeds to die at time n+1 and give birth, independently from the other particles of generation n, to a random number of particles at random positions. In a first chapter, we define in details the branching random walk model and some key elements of the scientific research on this model, including the study of the additive martingale. This martingale can be stuided through its convergence towards a limit that may be trivial, raising the question of an appropriate scaling, called Seneta-Heyde sclaing, in the case the limit is trivial. The additive martingale can also be studied with stochastic recursive equations lezading to fixed points equations in law. This latter question is adressed in some unpublished works from the first year of PhD, in continuioty with works from the masters thesis. The second chapter is a translation in english of some sections of the preivous chapter so that every reader can grasp the key elements and goals of this manuscript.In a third chapter, we present a new proof developed with Pascal Maillard for Aîdékon and Shi's theorem on the Seneta-Heyde scaling of the critical additive martingale in the finite variance case. This new proof no longer need a peeling lemma and the use of second moment arguments and prefers studying the conditional Laplace transform. the properties of some renewal functions allow a much more general approach without the need to foucs to much on the derivative martingale. This is also illustrated in a fourth chapter where in new works with Pascal Maillard, we find the Seneta-Heyde scaling for the critical additive martingale in the case where the spinal random walk is in the attraction domain of a stable law. We then observe that the renewal functions provide us with a better suited candidate for this study than the derivative artingale, which is no longer always a martingale in this context.Finally, the fifth chapter focus on the question of the optimality of the assumptions made in the preivous chapter concerning the non-triviality of the limit obtained with the Seneta-Heyde scaling
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Tokushige, Yuki. "Random Walks on random trees and hyperbolic groups: trace processes on boundaries at infinity and the speed of biased random walks." Kyoto University, 2019. http://hdl.handle.net/2433/242580.

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De, Bacco Caterina. "Decentralized network control, optimization and random walks on networks." Thesis, Paris 11, 2015. http://www.theses.fr/2015PA112164/document.

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Dans les dernières années, plusieurs problèmes ont été étudiés à l'interface entre la physique statistique et l'informatique. La raison étant que, souvent, ces problèmes peuvent être réinterprétés dans le langage de la physique des systèmes désordonnés, où un grand nombre de variables interagit à travers champs locales qui dépendent de l'état du quartier environnant. Parmi les nombreuses applications de l'optimisation combinatoire le routage optimal sur les réseaux de communication est l'objet de la première partie de la thèse. Nous allons exploiter la méthode de la cavité pour formuler des algorithmes efficaces de type ‘’message-passing’’ et donc résoudre plusieurs variantes du problème grâce à sa mise en œuvre numérique. Dans un deuxième temps, nous allons décrire un modèle pour approcher la version dynamique de la méthode de la cavité, ce qui permet de diminuer la complexité du problème de l'exponentielle de polynôme dans le temps. Ceci sera obtenu en utilisant le formalisme de ‘’Matrix Product State’’ de la mécanique quantique.Un autre sujet qui a suscité beaucoup d'intérêt en physique statistique de processus dynamiques est la marche aléatoire sur les réseaux. La théorie a été développée depuis de nombreuses années dans le cas que la topologie dessous est un réseau de dimension d. Au contraire le cas des réseaux aléatoires a été abordé que dans la dernière décennie, laissant de nombreuses questions encore ouvertes pour obtenir des réponses. Démêler plusieurs aspects de ce thème fera l'objet de la deuxième partie de la thèse. En particulier, nous allons étudier le nombre moyen de sites distincts visités au cours d'une marche aléatoire et caractériser son comportement en fonction de la topologie du graphe. Enfin, nous allons aborder les événements rares statistiques associées aux marches aléatoires sur les réseaux en utilisant le ‘’Large deviations formalism’’. Deux types de transitions de phase dynamiques vont se poser à partir de simulations numériques. Nous allons conclure décrivant les principaux résultats d'une œuvre indépendante développée dans le cadre de la physique hors de l'équilibre. Un système résoluble en deux particules browniens entouré par un bain thermique sera étudiée fournissant des détails sur une interaction à médiation par du bain résultant de la présence du bain
In the last years several problems been studied at the interface between statistical physics and computer science. The reason being that often these problems can be reinterpreted in the language of physics of disordered systems, where a big number of variables interacts through local fields dependent on the state of the surrounding neighborhood. Among the numerous applications of combinatorial optimisation the optimal routing on communication networks is the subject of the first part of the thesis. We will exploit the cavity method to formulate efficient algorithms of type message-passing and thus solve several variants of the problem through its numerical implementation. At a second stage, we will describe a model to approximate the dynamic version of the cavity method, which allows to decrease the complexity of the problem from exponential to polynomial in time. This will be obtained by using the Matrix Product State formalism of quantum mechanics. Another topic that has attracted much interest in statistical physics of dynamic processes is the random walk on networks. The theory has been developed since many years in the case the underneath topology is a d-dimensional lattice. On the contrary the case of random networks has been tackled only in the past decade, leaving many questions still open for answers. Unravelling several aspects of this topic will be the subject of the second part of the thesis. In particular we will study the average number of distinct sites visited during a random walk and characterize its behaviour as a function of the graph topology. Finally, we will address the rare events statistics associated to random walks on networks by using the large-deviations formalism. Two types of dynamic phase transitions will arise from numerical simulations, unveiling important aspects of these problems. We will conclude outlining the main results of an independent work developed in the context of out-of-equilibrium physics. A solvable system made of two Brownian particles surrounded by a thermal bath will be studied providing details about a bath-mediated interaction arising for the presence of the bath
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Maddalena, Daniela. "Stationary states in random walks on networks." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016. http://amslaurea.unibo.it/10170/.

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In this thesis we dealt with the problem of describing a transportation network in which the objects in movement were subject to both finite transportation capacity and finite accomodation capacity. The movements across such a system are realistically of a simultaneous nature which poses some challenges when formulating a mathematical description. We tried to derive such a general modellization from one posed on a simplified problem based on asyncronicity in particle transitions. We did so considering one-step processes based on the assumption that the system could be describable through discrete time Markov processes with finite state space. After describing the pre-established dynamics in terms of master equations we determined stationary states for the considered processes. Numerical simulations then led to the conclusion that a general system naturally evolves toward a congestion state when its particle transition simultaneously and we consider one single constraint in the form of network node capacity. Moreover the congested nodes of a system tend to be located in adjacent spots in the network, thus forming local clusters of congested nodes.
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Gabrysch, Katja. "On Directed Random Graphs and Greedy Walks on Point Processes." Doctoral thesis, Uppsala universitet, Analys och sannolikhetsteori, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-305859.

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This thesis consists of an introduction and five papers, of which two contribute to the theory of directed random graphs and three to the theory of greedy walks on point processes.           We consider a directed random graph on a partially ordered vertex set, with an edge between any two comparable vertices present with probability p, independently of all other edges, and each edge is directed from the vertex with smaller label to the vertex with larger label. In Paper I we consider a directed random graph on ℤ2 with the vertices ordered according to the product order and we show that the limiting distribution of the centered and rescaled length of the longest path from (0,0) to (n, [na] ), a<3/14, is the Tracy-Widom distribution. In Paper II we show that, under a suitable rescaling, the closure of vertex 0 of a directed random graph on ℤ with edge probability n−1 converges in distribution to the Poisson-weighted infinite tree. Moreover, we derive limit theorems for the length of the longest path of the Poisson-weighted infinite tree.           The greedy walk is a deterministic walk on a point process that always moves from its current position to the nearest not yet visited point. Since the greedy walk on a homogeneous Poisson process on the real line, starting from 0, almost surely does not visit all points, in Paper III we find the distribution of the number of visited points on the negative half-line and the distribution of the index at which the walk achieves its minimum. In Paper IV we place homogeneous Poisson processes first on two intersecting lines and then on two parallel lines and we study whether the greedy walk visits all points of the processes. In Paper V we consider the greedy walk on an inhomogeneous Poisson process on the real line and we determine sufficient and necessary conditions on the mean measure of the process for the walk to visit all points.
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Bernergård, Zandra. "Connection between discrete time random walks and stochastic processes by Donsker's Theorem." Thesis, Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-48719.

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In this paper we will investigate the connection between a random walk and a continuous time stochastic process. Donsker's Theorem states that a random walk under certain conditions will converge to a Wiener process. We will provide a detailed proof of this theorem which will be used to prove that a geometric random walk converges to a geometric Brownian motion.
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Books on the topic "Random walk processses"

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A random walk down Wall Street. 4th ed. New York: Norton, 1985.

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Ibe, Oliver C. Elements of Random Walk and Diffusion Processes. Hoboken, NJ: John Wiley & Sons, Inc, 2013. http://dx.doi.org/10.1002/9781118618059.

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Random walk and the heat equation. Providence, R.I: American Mathematical Society, 2010.

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Hughes, B. D. Random walks and random environments. Oxford: Clarendon Press, 1995.

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Prabhu, N. U. (Narahari Umanath), 1924- and Tang Loon Ching, eds. Markov-modulated processes & semiregenerative phenomena. Singapore: World Scientific, 2009.

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Random walks of infinitely many particles. Singapore: World Scientific, 1994.

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David, Gaspari George, ed. Elements of the random walk: An introduction for advanced students and researchers. Cambridge: Cambridge University Press, 2004.

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Statistical mechanics and random walks: Principles, processes, and applications. New York: Nova Science Publishers, 2012.

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Lawler, Gregory F. Intersections of Random Walks. New York, NY: Springer New York, 2013.

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R. W. van der Hofstad. One-dimensional random polymers. Amsterdam, The Netherlands: CWI, 1998.

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Book chapters on the topic "Random walk processses"

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Korosteleva, Olga. "Random Walk." In Stochastic Processes with R, 43–60. Boca Raton: Chapman and Hall/CRC, 2022. http://dx.doi.org/10.1201/9781003244288-2.

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Ney, Peter. "Branching Random Walk." In Spatial Stochastic Processes, 3–22. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0451-0_1.

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Gut, Allan. "Renewal Processes and Random Walks." In Stopped Random Walks, 46–73. New York, NY: Springer New York, 1988. http://dx.doi.org/10.1007/978-1-4757-1992-5_3.

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Gut, Allan. "Renewal Processes and Random Walks." In Stopped Random Walks, 49–77. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-0-387-87835-5_2.

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Bosq, Denis, and Hung T. Nguyen. "Random Walks." In A Course in Stochastic Processes, 117–46. Dordrecht: Springer Netherlands, 1996. http://dx.doi.org/10.1007/978-94-015-8769-3_6.

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Resnick, Sidney I. "The General Random Walk." In Adventures in Stochastic Processes, 558–612. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0387-2_7.

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Schwarz, Wolf. "More General Diffusion Processes." In Random Walk and Diffusion Models, 121–40. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-12100-5_5.

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Schinazi, Rinaldo B. "A Branching Random Walk." In Classical and Spatial Stochastic Processes, 231–49. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1869-0_12.

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Gallager, Robert G. "Random Walks and Martingales." In Discrete Stochastic Processes, 223–63. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4615-2329-1_7.

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Schinazi, Rinaldo B. "Continuous Time Branching Random Walk." In Classical and Spatial Stochastic Processes, 135–52. Boston, MA: Birkhäuser Boston, 1999. http://dx.doi.org/10.1007/978-1-4612-1582-0_6.

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Conference papers on the topic "Random walk processses"

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HUANG, WEN-JANG, and CHUEN-DOW HUANG. "A STUDY OF INVERSES OF THINNED RENEWAL PROCESSES." In Random Walk, Sequential Analysis and Related Topics - A Festschrift in Honor of Yuan-Shih Chow. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772558_0006.

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LIN, ZHENGYAN, and DEGUI LI. "THE L1-NORM KERNEL ESTIMATOR OF CONDITIONAL MEDIAN FOR STATIONARY PROCESSES." In Random Walk, Sequential Analysis and Related Topics - A Festschrift in Honor of Yuan-Shih Chow. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772558_0019.

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GORENFLO, R., F. MAINARDI, and A. VIVOLI. "SUBORDINATION IN FRACTIONAL DIFFUSION PROCESSES VIA CONTINUOUS TIME RANDOM WALK." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0043.

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Andrade, Matheus Guedes de, Franklin De Lima Marquezino, and Daniel Ratton Figueiredo. "Characterizing the Relationship Between Unitary Quantum Walks and Non-Homogeneous Random Walks." In Concurso de Teses e Dissertações da SBC. Sociedade Brasileira de Computação, 2021. http://dx.doi.org/10.5753/ctd.2021.15756.

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Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the relationship between quantum and random walks has been recently discussed in specific scenarios, this work establishes a formal equivalence between the two processes on arbitrary finite graphs and general conditions for shift and coin operators. It requires empowering random walks with time heterogeneity, where the transition probability of the walker is non-uniform and time dependent. The equivalence is obtained by equating the probability of measuring the quantum walk on a given node of the graph and the probability that the random walk is at that same node, for all nodes and time steps. The first result establishes procedure for a stochastic matrix sequence to induce a random walk that yields the exact same vertex probability distribution sequence of any given quantum walk, including the scenario with multiple interfering walkers. The second result establishes a similar procedure in the opposite direction. Given any random walk, a time-dependent quantum walk with the exact same vertex probability distribution is constructed. Interestingly, the matrices constructed by the first procedure allows for a different simulation approach for quantum walks where node samples respect neighbor locality and convergence is guaranteed by the law of large numbers, enabling efficient (polynomial-time) sampling of quantum graph trajectories. Furthermore, the complexity of constructing this sequence of matrices is discussed in the general case.
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Orlowski, M. "Zero-flux boundary condition in a two-probability-parameter random walk model." In IEEE International Conference on Simulation of Semiconductor Processes and Devices. IEEE, 2003. http://dx.doi.org/10.1109/sispad.2003.1233650.

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Ren, Jing, and Sriram Sundararajan. "Microfluidic Channel Fabrication With Tailored Wall Roughness." In ASME 2012 International Manufacturing Science and Engineering Conference collocated with the 40th North American Manufacturing Research Conference and in participation with the International Conference on Tribology Materials and Processing. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/msec2012-7328.

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Realistic random roughness of channel surfaces is known to affect the fluid flow behavior in microscale fluidic devices. This has relevance particularly for applications involving non-Newtonian fluids, such as biomedical lab-on-chip devices. In this study, a surface texturing process was developed and integrated into microfluidic channel fabrication. The process combines colloidal masking and Reactive Ion Etching (RIE) for generating random surfaces with desired roughness parameters on the micro/nanoscale. The surface texturing process was shown to be able to tailor the random surface roughness on quartz. A Large range of particle coverage (around 6% to 67%) was achieved using dip coating and drop casting methods using a polystyrene colloidal solution. A relation between the amplitude roughness, autocorrelation length, etch depth and particle coverage of the processed surface was built. Experimental results agreed reasonably well with model predictions. The processed substrate was further incorporated into microchannel fabrication. Final device with designed wall roughness was tested and proved a satisfying sealing performance.
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Lee, Geon, Minyoung Choe, and Kijung Shin. "HashNWalk: Hash and Random Walk Based Anomaly Detection in Hyperedge Streams." In Thirty-First International Joint Conference on Artificial Intelligence {IJCAI-22}. California: International Joint Conferences on Artificial Intelligence Organization, 2022. http://dx.doi.org/10.24963/ijcai.2022/296.

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Sequences of group interactions, such as emails, online discussions, and co-authorships, are ubiquitous; and they are naturally represented as a stream of hyperedges (i.e., sets of nodes). Despite its broad potential applications, anomaly detection in hypergraphs (i.e., sets of hyperedges) has received surprisingly little attention, compared to anomaly detection in graphs. While it is tempting to reduce hypergraphs to graphs and apply existing graph-based methods, according to our experiments, taking higher-order structures of hypergraphs into consideration is worthwhile. We propose HashNWalk, an incremental algorithm that detects anomalies in a stream of hyperedges. It maintains and updates a constant-size summary of the structural and temporal information about the input stream. Using the summary, which is the form of a proximity matrix, HashNWalk measures the anomalousness of each new hyperedge as it appears. HashNWalk is (a) Fast: it processes each hyperedge in near real-time and billions of hyperedges within a few hours, (b) Space Efficient: the size of the maintained summary is a user-specific constant, (c) Effective: it successfully detects anomalous hyperedges in real-world hypergraphs.
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Korolev, Victor, Vladimir Bening, Lilya Zaks, and Alexander Zeifman. "On Convergence Of Random Walks Having Jumps With Finite Variances To Stable Levy Processes." In 27th Conference on Modelling and Simulation. ECMS, 2013. http://dx.doi.org/10.7148/2013-0601.

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Sevostyanov, Petr A., Tatyana A. Samoilova, and Ekaterina N. Vakhromeeva. "Modeling of the dynamics of computer memory filling." In INTERNATIONAL SCIENTIFIC-TECHNICAL SYMPOSIUM (ISTS) «IMPROVING ENERGY AND RESOURCE-EFFICIENT AND ENVIRONMENTAL SAFETY OF PROCESSES AND DEVICES IN CHEMICAL AND RELATED INDUSTRIES». The Kosygin State University of Russia, 2021. http://dx.doi.org/10.37816/eeste-2021-2-84-88.

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Wang, Yan. "Accelerating Stochastic Dynamics Simulation With Continuous-Time Quantum Walks." In ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/detc2016-59420.

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Stochastic diffusion is a general phenomenon observed in various national and engineering systems. It is typically modeled by either stochastic differential equation (SDE) or Fokker-Planck equation (FPE), which are equivalent approaches. Path integral is an accurate and effective method to solve FPEs. Yet, computational efficiency is the common challenge for path integral and other numerical methods, include time and space complexities. Previously, one-dimensional continuous-time quantum walk was used to simulate diffusion. By combining quantum diffusion and random diffusion, the new approach can accelerate the simulation with longer time steps than those in path integral. It was demonstrated that simulation can be dozens or even hundreds of times faster. In this paper, a new generic quantum operator is proposed to simulate drift-diffusion processes in high-dimensional space, which combines quantum walks on graphs with traditional path integral approaches. Probability amplitudes are computed efficiently by spectral analysis. The efficiency of the new method is demonstrated with stochastic resonance problems.
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Reports on the topic "Random walk processses"

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Young, Richard M. Modeling Random Walk Processes In Human Concept Learning. Fort Belvoir, VA: Defense Technical Information Center, May 2006. http://dx.doi.org/10.21236/ada462700.

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