Relevant bibliographies by topics / Hitting time of random walk

Academic literature on the topic 'Hitting time of random walk'

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Published: 9 March 2023
Last updated: 10 March 2023

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Journal articles on the topic "Hitting time of random walk"

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Emms, D., R. Wilson, and E. Hancock. "Graph embedding using quantum hitting time." Quantum Information and Computation 9, no. 3&4 (March 2009): 231–54. http://dx.doi.org/10.26421/qic9.3-4-4.

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In this paper, we explore analytically and experimentally a quasi-quantum analogue of the hitting time of the continuous-time quantum walk on a graph. For the classical random walk, the hitting time has been shown to be robust to errors in edge weight structure and to lead to spectral clustering algorithms with improved performance. Our analysis shows that the quasi-quantum analogue of the hitting time of the continuous-time quantum walk can be determined via integrals of the Laplacian spectrum, calculated using Gauss-Laguerre quadrature. We analyse the quantum hitting times with reference to their classical counterpart. Specifically, we explore the graph embeddings that preserve hitting time. Experimentally, we show that the quantum hitting times can be used to emphasise cluster-structure.
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Lardizabal, Carlos F. "Open quantum random walks and the mean hitting time formula." Quantum Information and Computation 17, no. 1&2 (January 2017): 79–105. http://dx.doi.org/10.26421/qic17.1-2-5.

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We make use of the Open Quantum Random Walk setting due to S. Attal, F. Petruccione, C. Sabot and I. Sinayskiy in order to discuss hitting times and a quantum version of the Mean Hitting Time Formula from classical probability theory. We study an open quantum notion of hitting probability on a finite collection of sites and with this we are able to describe the problem in terms of linear maps and its matrix representations. After setting an open quantum version of the fundamental matrix for ergodic Markov chains we are able to prove our main result and as consequence a version of the Random Target Lemma. We also study a mean hitting time formula in terms of the minimal polynomial associated to the matrix representation of the quantum walk. We discuss applications of the results to open quantum dynamics on graphs together with open questions.
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Aldous, David. "Hitting times for random walks on vertex-transitive graphs." Mathematical Proceedings of the Cambridge Philosophical Society 106, no. 1 (July 1989): 179–91. http://dx.doi.org/10.1017/s0305004100068079.

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AbstractFor random walks on finite graphs, we record some equalities, inequalities and limit theorems (as the size of graph tends to infinity) which hold for vertex-transitive graphs but not for general regular graphs. The main result is a sharp condition for asymptotic exponentiality of the hitting time to a single vertex. Another result is a lower bound for the coefficient of variation of hitting times. Proofs exploit the complete monotonicity properties of the associated continuous-time walk.
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Meerschaert, Mark M., and Hans-Peter Scheffler. "Limit theorems for continuous-time random walks with infinite mean waiting times." Journal of Applied Probability 41, no. 3 (September 2004): 623–38. http://dx.doi.org/10.1239/jap/1091543414.

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A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.
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Meerschaert, Mark M., and Hans-Peter Scheffler. "Limit theorems for continuous-time random walks with infinite mean waiting times." Journal of Applied Probability 41, no. 03 (September 2004): 623–38. http://dx.doi.org/10.1017/s002190020002043x.

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A continuous-time random walk is a simple random walk subordinated to a renewal process used in physics to model anomalous diffusion. In this paper we show that, when the time between renewals has infinite mean, the scaling limit is an operator Lévy motion subordinated to the hitting time process of a classical stable subordinator. Density functions for the limit process solve a fractional Cauchy problem, the generalization of a fractional partial differential equation for Hamiltonian chaos. We also establish a functional limit theorem for random walks with jumps in the strict generalized domain of attraction of a full operator stable law, which is of some independent interest.
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Afanasyev, Valeriy I. "On the non-recurrent random walk in a random environment." Discrete Mathematics and Applications 28, no. 3 (June 26, 2018): 139–56. http://dx.doi.org/10.1515/dma-2018-0014.

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Bertoin, Jean. "On overshoots and hitting times for random walks." Journal of Applied Probability 36, no. 2 (June 1999): 593–600. http://dx.doi.org/10.1239/jap/1032374474.

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Consider an oscillating integer valued random walk up to the first hitting time of some fixed integer x > 0. Suppose there is a fee to be paid each time the random walk crosses the level x, and that the amount corresponds to the overshoot. We determine the distribution of the sum of these fees in terms of the renewal functions of the ascending and descending ladder heights. The proof is based on the observation that some path transformation of the random walk enables us to translate the problem in terms of the intersection of certain regenerative sets.
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Bertoin, Jean. "On overshoots and hitting times for random walks." Journal of Applied Probability 36, no. 02 (June 1999): 593–600. http://dx.doi.org/10.1017/s0021900200017344.

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Consider an oscillating integer valued random walk up to the first hitting time of some fixed integer x > 0. Suppose there is a fee to be paid each time the random walk crosses the level x, and that the amount corresponds to the overshoot. We determine the distribution of the sum of these fees in terms of the renewal functions of the ascending and descending ladder heights. The proof is based on the observation that some path transformation of the random walk enables us to translate the problem in terms of the intersection of certain regenerative sets.
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Haslegrave, John, Thomas Sauerwald, and John Sylvester. "Time Dependent Biased Random Walks." ACM Transactions on Algorithms 18, no. 2 (April 30, 2022): 1–30. http://dx.doi.org/10.1145/3498848.

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We study the biased random walk where at each step of a random walk a “controller” can, with a certain small probability, move the walk to an arbitrary neighbour. This model was introduced by Azar et al. [STOC’1992]; we extend their work to the time dependent setting and consider cover times of this walk. We obtain new bounds on the cover and hitting times. Azar et al. conjectured that the controller can increase the stationary probability of a vertex from p to p 1-ε ; while this conjecture is not true in full generality, we propose a best-possible amended version of this conjecture and confirm it for a broad class of graphs. We also consider the problem of computing an optimal strategy for the controller to minimise the cover time and show that for directed graphs determining the cover time is PSPACE -complete.
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Kalikova, A. "Statistical analysis of random walks on network." Scientific Journal of Astana IT University, no. 5 (July 27, 2021): 77–83. http://dx.doi.org/10.37943/aitu.2021.99.34.007.

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This paper describes an investigation of analytical formulas for parameters in random walks. Random walks are used to model situations in which an object moves in a sequence of steps in randomly chosen directions. Given a graph and a starting point, we select a neighbor of it at random, and move to this neighbor; then we select a neighbor of this point at random, and move to it etc. It is a fundamental dynamic process that arise in many models in mathematics, physics, informatics and can be used to model random processes inherent to many important applications. Different aspects of the theory of random walks on graphs are surveyed. In particular, estimates on the important parameters of hitting time, commute time, cover time are discussed in various works. In some papers, authors have derived an analytical expression for the distribution of the cover time for a random walk over an arbitrary graph that was tested for small values of n. However, this work will show the simplified analytical expressions for distribution of hitting time, commute time, cover time for bigger values of n. Moreover, this work will present the probability mass function and the cumulative distribution function for hitting time, commute time.
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Dissertations / Theses on the topic "Hitting time of random walk"

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BORRELLO, DAVIDE. "Interacting particle systems: stochastic order, attractiveness and random walks on small world graphs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2009. http://hdl.handle.net/10281/7467.

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The main subject of the thesis is concerned with interacting particle systems, which are classes of spatio-temporal stochastic processes describing the evolution of particles in interaction with each other. The particles move on a finite or infinite discrete space and on each element of this space the state of the configuration is integer valued. Configurations of particles evolve in continuous time according to a Markov process. Here the space is either the infinite deterministic d-dimensional lattice or a random graph given by the finite d-dimensional torus with random matchings. In Part I we investigate the stochastic order in a particle system with multiple births, deaths and jumps on the d-dimensional lattice: stochastic order is a key tool to understand the ergodic properties of a system. We give applications on biological models of spread of epidemics and metapopulation dynamics systems. In Part II we analyse the coalescing random walk in a class of finite random graphs modeling social networks, the small world graphs. We derive the law of the meeting time of two random walks on small world graphs and we use this result to understand the role of random connections in meeting time of random walks and to investigate the behavior of coalescing random walks.
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Santos, Raqueline Azevedo Medeiros. "Cadeias de Markov Quânticas." Laboratório Nacional de Computação Científica, 2010. http://www.lncc.br/tdmc/tde_busca/arquivo.php?codArquivo=199.

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Em Ciência da Computação, os caminhos aleatórios são utilizados em algoritmos randômicos, especialmente em algoritmos de busca, quando desejamos encontrar um estado marcado numa cadeia de Markov. Nesse tipo de algoritmo é interessante estudar o Tempo de Alcance, que está associado a sua complexidade computacional. Nesse contexto, descrevemos a teoria clássica de cadeias de Markov e caminhos aleatórios, assim como o seu análogo quântico. Dessa forma, definimos o Tempo de Alcance sob o escopo das cadeias de Markov quânticas. Além disso, expressões analíticas calculadas para o tempo de Alcance quântico e para a probabilidade de encontrarmos um elemento marcado num grafo completo são apresentadas como os novos resultados dessa dissertação.
In Computer Science, random walks are used in randomized algorithms, specially in search algorithms, where we desire to find a marked state in a Markov chain.In this type of algorithm,it is interesting to study the Hitting Time, which is associated to its computational complexity. In this context, we describe the classical theory of Markov chains and random walks,as well as their quantum analogue.In this way,we define the Hitting Time under the scope of quantum Markov chains. Moreover, analytical expressions calculated for the quantum Hitting Time and for the probability of finding a marked element on the complete graph are presented as the new results of this dissertation.
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Gubiec, Tomasz, and Ryszard Kutner. "Two-step memory within Continuous Time Random Walk." Universitätsbibliothek Leipzig, 2015. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-183316.

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Gubiec, Tomasz, and Ryszard Kutner. "Two-step memory within Continuous Time Random Walk." Diffusion fundamentals 20 (2013) 64, S. 1, 2013. https://ul.qucosa.de/id/qucosa%3A13643.

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Chang, Qiang. "Continuous-time random-walk simulation of surface kinetics." The Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc_num=osu1166592142.

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Katzenbeisser, Walter, and Wolfgang Panny. "Simple Random Walk Statistics. Part I: Discrete Time Results." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 1990. http://epub.wu.ac.at/1078/1/document.pdf.

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In a famous paper Dwass [I9671 proposed a method to deal with rank order statistics, which constitutes a unifying framework to derive various distributional results. In the present paper an alternative method is presented, which allows to extend Dwass's results in several ways, viz. arbitrary endpoints, horizontal steps, and arbitrary probabilities for the three step types. Regarding these extensions the pertaining rank order statistics are extended as well to simple random walk statistics. This method has proved appropriate to generalize all results given by Dwass. Moreover, these discrete time results can be taken as a starting point to derive the corresponding results for randomized random walks by means of a limiting process. (author's abstract)
Series: Forschungsberichte / Institut für Statistik
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Li, Chao. "Option pricing with generalized continuous time random walk models." Thesis, Queen Mary, University of London, 2016. http://qmro.qmul.ac.uk/xmlui/handle/123456789/23202.

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The pricing of options is one of the key problems in mathematical finance. In recent years, pricing models that are based on the continuous time random walk (CTRW), an anomalous diffusive random walk model widely used in physics, have been introduced. In this thesis, we investigate the pricing of European call options with CTRW and generalized CTRW models within the Black-Scholes framework. Here, the non-Markovian character of the underlying pricing model is manifest in Black-Scholes PDEs with fractional time derivatives containing memory terms. The inclusion of non-zero interest rates leads to a distinction between different types of \forward" and \backward" options, which are easily mapped onto each other in the standard Markovian framework, but exhibit significant dfferences in the non-Markovian case. The backward-type options require us in particular to include the multi-point statistics of the non-Markovian pricing model. Using a representation of the CTRW in terms of a subordination (time change) of a normal diffusive process with an inverse L evy-stable process, analytical results can be obtained. The extension of the formalism to arbitrary waiting time distributions and general payoff functions is discussed. The pricing of path-dependent Asian options leads to further distinctions between different variants of the subordination. We obtain analytical results that relate the option price to the solution of generalized Feynman-Kac equations containing non-local time derivatives such as the fractional substantial derivative. Results for L evy-stable and tempered L evy-stable subordinators, power options, arithmetic and geometric Asian options are presented.
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Niemann, Markus. "From Anomalous Deterministic Diffusion to the Continuous-Time Random Walk." Wuppertal Universitätsbibliothek Wuppertal, 2010. http://d-nb.info/1000127621/34.

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Lau, Hon Wai. "Random walk in networks : first passage time and speed analysis /." View abstract or full-text, 2009. http://library.ust.hk/cgi/db/thesis.pl?PHYS%202009%20LAU.

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Allen, Andrew. "A Random Walk Version of Robbins' Problem." Thesis, University of North Texas, 2018. https://digital.library.unt.edu/ark:/67531/metadc1404568/.

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Robbins' problem is an optimal stopping problem where one seeks to minimize the expected rank of their observations among all observations. We examine random walk analogs to Robbins' problem in both discrete and continuous time. In discrete time, we consider full information and relative ranks versions of this problem. For three step walks, we give the optimal stopping rule and the expected rank for both versions. We also give asymptotic upper bounds for the expected rank in discrete time. Finally, we give upper and lower bounds for the expected rank in continuous time, and we show that the expected rank in the continuous time problem is at least as large as the normalized asymptotic expected rank in the full information discrete time version.
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Books on the topic "Hitting time of random walk"

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Nicolas, Christian. Random walk. London: Architectural Association Students Union, 1998.

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A random walk down Wall Street: The time-tested strategy for successful investing. New York: W.W. Norton & Co., 2011.

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A random walk down Wall Street: The time-tested strategy for successful investing. New York: W.W. Norton, 2012.

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A random walk down Wall Street: The time-tested strategy for successful investing. 9th ed. New York: W. W. Norton, 2007.

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Malkiel, Burton Gordon. A random walk down Wall Street: The time-tested strategy for successful investing. New York: W.W. Norton, 2003.

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Malkiel, Burton Gordon. A random walk down Wall Street: The time-tested strategy for successful investing. New York: W.W. Norton, 2003.

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A random walk down Wall Street: The time-tested strategy for successful investing. 9th ed. New York: W. W. Norton, 2007.

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A random walk down Wall Street: The time-tested strategy for successful investing. New York: W.W. Norton, 2003.

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A random walk down Wall Street: The time-tested strategy for successful investing. London: W.W.Norton, 2004.

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Luger, Richard. Exact non-parametric tests for a random walk with unknown drift under conditional heteroscedasticity. Ottawa, Ont: Bank of Canada, 2001.

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Book chapters on the topic "Hitting time of random walk"

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Santha, Miklos. "Quantization of Random Walks: Search Algorithms and Hitting Time." In Computer Science – Theory and Applications, 343. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-13182-0_33.

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Zhang, Yi, Daniel Boley, John Harwell, and Maria Gini. "A Correlated Random Walk Model to Rapidly Approximate Hitting Time Distributions in Multi-robot Systems." In Intelligent Autonomous Systems 17, 724–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-22216-0_48.

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Jin, Bangti. "Continuous Time Random Walk." In Fractional Differential Equations, 3–18. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-76043-4_1.

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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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Marti, Gautier, Frank Nielsen, Philippe Very, and Philippe Donnat. "Clustering Random Walk Time Series." In Lecture Notes in Computer Science, 675–84. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-25040-3_72.

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Ethier, S. N. "Absorption Time Distribution for an Asymmetric Random Walk." In Institute of Mathematical Statistics Collections, 31–40. Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2008. http://dx.doi.org/10.1214/074921708000000282.

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Kotulskil, Marcin, and Karina Weron. "Random Walk Approach to Relaxation in Disordered Systems." In Athens Conference on Applied Probability and Time Series Analysis, 379–88. New York, NY: Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4612-0749-8_27.

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Avrachenkov, Konstantin, and Ilya Bogdanov. "Analysis of Relaxation Time in Random Walk with Jumps." In Lecture Notes in Computer Science, 70–82. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-92871-5_6.

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Song, Yifan, Darong Lai, Zhihong Chong, and Zeyuan Pan. "Dynamic Network Embedding by Time-Relaxed Temporal Random Walk." In Neural Information Processing, 426–37. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-92185-9_35.

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Zhao, Chen, and Mihail L. Sichitiu. "Contact Time in Random Walk and Random Waypoint: Dichotomy in Tail Distribution." In Ad Hoc Networks, 333–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11723-7_22.

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Conference papers on the topic "Hitting time of random walk"

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Oosthuizen, Joubert, and Stephan Wagner. "On the distribution of random walk hitting times in random trees." In 2017 Proceedings of the Fourteenth Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2017. http://dx.doi.org/10.1137/1.9781611974775.7.

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Zhang, Zuobai, Wanyue Xu, and Zhongzhi Zhang. "Nearly Linear Time Algorithm for Mean Hitting Times of Random Walks on a Graph." In WSDM '20: The Thirteenth ACM International Conference on Web Search and Data Mining. New York, NY, USA: ACM, 2020. http://dx.doi.org/10.1145/3336191.3371777.

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Magalang, Juan Antonio, and Jose Perico Esguerra. "Hitting, commute, and cover time distributions for resetting random walks on circular graphs." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 12th International On-line Conference for Promoting the Application of Mathematics in Technical and Natural Sciences - AMiTaNS’20. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0029722.

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Devulapalli, Pramith, Bistra Dilkina, and Yexiang Xue. "Embedding Conjugate Gradient in Learning Random Walks for Landscape Connectivity Modeling in Conservation." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/598.

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Models capturing parameterized random walks on graphs have been widely adopted in wildlife conservation to study species dispersal as a function of landscape features. Learning the probabilistic model empowers ecologists to understand animal responses to conservation strategies. By exploiting the connection between random walks and simple electric networks, we show that learning a random walk model can be reduced to finding the optimal graph Laplacian for a circuit. We propose a moment matching strategy that correlates the model’s hitting and commuting times with those observed empirically. To find the best Laplacian, we propose a neural network capable of back-propagating gradients through the matrix inverse in an end-to-end fashion. We developed a scalable method called CGInv which back-propagates the gradients through a neural network encoding each layer as a conjugate gradient iteration. To demonstrate its effectiveness, we apply our computational framework to applications in landscape connectivity modeling. Our experiments successfully demonstrate that our framework effectively and efficiently recovers the ground-truth configurations.
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Magniez, Frederic, Ashwin Nayak, Peter C. Richter, and Miklos Santha. "On the hitting times of quantum versus random walks." In Proceedings of the Twentieth Annual ACM-SIAM Symposium on Discrete Algorithms. Philadelphia, PA: Society for Industrial and Applied Mathematics, 2009. http://dx.doi.org/10.1137/1.9781611973068.10.

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Yujun Yang. "Expected hitting times for simple random walks on wheel graphs." In 2011 International Conference on Multimedia Technology (ICMT). IEEE, 2011. http://dx.doi.org/10.1109/icmt.2011.6002460.

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Mastio, Guillaume, and Pérola Milman. "1D Discrete-Time Random Walk." In Quantum Information and Measurement. Washington, D.C.: OSA, 2017. http://dx.doi.org/10.1364/qim.2017.qt6a.31.

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MAINARDI, F., R. GORENFLO, D. MORETTI, and P. PARADISI. "RANDOM WALK MODELS FOR TIME-FRACTIONAL DIFFUSION." In Conference on Fractals 2002. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777720_0016.

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Ganguly, Shirshendu, and Yuval Peres. "Permuted Random Walk Exits Typically in Linear Time." In 2014 Proceedings of the Eleventh Workshop on Analytic Algorithmics and Combinatorics (ANALCO). Philadelphia, PA: Society for Industrial and Applied Mathematics, 2013. http://dx.doi.org/10.1137/1.9781611973204.7.

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Delfino, Ines, Maria Lepore, and Pietro L. Indovina. "Random walk analysis of time-resolved transmittance measurements." In Biomedical Optics 2003, edited by Britton Chance, Robert R. Alfano, Bruce J. Tromberg, Mamoru Tamura, and Eva M. Sevick-Muraca. SPIE, 2003. http://dx.doi.org/10.1117/12.476800.

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Reports on the topic "Hitting time of random walk"

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Pompeu, Gustavo, and José Luiz Rossi. Real/Dollar Exchange Rate Prediction Combining Machine Learning and Fundamental Models. Inter-American Development Bank, September 2022. http://dx.doi.org/10.18235/0004491.

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The study of the predictability of exchange rates has been a very recurring theme on the economics literature for decades, and very often is not possible to beat a random walk prediction, particularly when trying to forecast short time periods. Although there are several studies about exchange rate forecasting in general, predictions of specifically Brazilian real (BRL) to United States dollar (USD) exchange rates are very hard to find in the literature. The objective of this work is to predict the specific BRL to USD exchange rates by applying machine learning models combined with fundamental theories from macroeconomics, such as monetary and Taylor rule models, and compare the results to those of a random walk model by using the root mean squared error (RMSE) and the Diebold-Mariano (DM) test. We show that it is possible to beat the random walk by these metrics.
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