Relevant bibliographies by topics / Stochastic

Academic literature on the topic 'Stochastic'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 June 2024

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Journal articles on the topic "Stochastic"

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Engelbert, H. J., and V. P. Kurenok. "On Multidimensional SDEs Without Drift and with A Time-Dependent Diffusion Matrix." Georgian Mathematical Journal 7, no. 4 (December 2000): 643–64. http://dx.doi.org/10.1515/gmj.2000.643.

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Abstract We study multidimensional stochastic equations where x o is an arbitrary initial state, W is a d-dimensional Wiener process and is a measurable diffusion coefficient. We give sufficient conditions for the existence of weak solutions. Our main result generalizes some results obtained by A. Rozkosz and L. Słomiński [Stochastics Stochasties Rep. 42: 199–208, 1993] and T. Senf [Stochastics Stochastics Rep. 43: 199–220, 1993] for the existence of weak solutions of one-dimensional stochastic equations and also some results by A. Rozkosz and L. Słomiński [Stochastic Process. Appl. 37: 187–197, 1991], [Stochastic Process. Appl. 68: 285–302, 1997] for multidimensional equations. Finally, we also discuss the homogeneous case.
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Luo, Mei-Ju, and Yuan Lu. "Properties of Expected Residual Minimization Model for a Class of Stochastic Complementarity Problems." Journal of Applied Mathematics 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/497586.

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Expected residual minimization (ERM) model which minimizes an expected residual function defined by an NCP function has been studied in the literature for solving stochastic complementarity problems. In this paper, we first give the definitions of stochasticP-function, stochasticP0-function, and stochastic uniformlyP-function. Furthermore, the conditions such that the function is a stochasticPP0-function are considered. We then study the boundedness of solution set and global error bounds of the expected residual functions defined by the “Fischer-Burmeister” (FB) function and “min” function. The conclusion indicates that solutions of the ERM model are robust in the sense that they may have a minimum sensitivity with respect to random parameter variations in stochastic complementarity problems. On the other hand, we employ quasi-Monte Carlo methods and derivative-free methods to solve ERM model.
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IMKELLER, PETER, and ADAM HUGH MONAHAN. "CONCEPTUAL STOCHASTIC CLIMATE MODELS." Stochastics and Dynamics 02, no. 03 (September 2002): 311–26. http://dx.doi.org/10.1142/s0219493702000443.

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From July 9 to 11, 2001, 50 researchers from the fields of climate dynamics and stochastic analysis met in Chorin, Germany, to discuss the idea of stochastic models of climate. The present issue of Stochastics and Dynamics collects several papers from this meeting. In this introduction to the volume, the idea of simple conceptual stochastic climate models is introduced amd recent results in the mathematically rigorous development and analysis of such models are reviewed. As well, a brief overview of the application of ideas from stochastic dynamics to simple models of the climate system is given.
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LIUM, ARNT-GUNNAR, TEODOR GABRIEL CRAINIC, and STEIN W. WALLACE. "CORRELATIONS IN STOCHASTIC PROGRAMMING: A CASE FROM STOCHASTIC SERVICE NETWORK DESIGN." Asia-Pacific Journal of Operational Research 24, no. 02 (April 2007): 161–79. http://dx.doi.org/10.1142/s0217595907001206.

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Deterministic models, even if used repeatedly, will not capture the essence of planning in an uncertain world. Flexibility and robustness can only be properly valued in models that use stochastics explicitly, such as stochastic optimization models. However, it may also be very important to capture how the random phenomena are related to one another. In this article we show how the solution to a stochastic service network design model depends heavily on the correlation structure among the random demands. The major goal of this paper is to discuss why this happens, and to provide insights into the effects of correlations on solution structures. We illustrate by an example.
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Liu, Caixia, Yingqi Zhang, and Huixia Sun. "Finite-TimeH∞Filtering for Singular Stochastic Systems." Journal of Applied Mathematics 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/615790.

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This paper addresses the problem of finite-timeH∞filtering for one family of singular stochastic systems with parametric uncertainties and time-varying norm-bounded disturbance. Initially, the definitions of singular stochastic finite-time boundedness and singular stochasticH∞finite-time boundedness are presented. Then, theH∞filtering is designed for the class of singular stochastic systems with or without uncertain parameters to ensure singular stochastic finite-time boundedness of the filtering error system and satisfy a prescribedH∞performance level in some given finite-time interval. Furthermore, sufficient criteria are presented for the solvability of the filtering problems by employing the linear matrix inequality technique. Finally, numerical examples are given to illustrate the validity of the proposed methodology.
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Zhang, Yingqi, Wei Cheng, Xiaowu Mu, and Caixia Liu. "Stochasticℋ∞Finite-Time Control of Discrete-Time Systems with Packet Loss." Mathematical Problems in Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/897481.

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This paper investigates the stochastic finite-time stabilization andℋ∞control problem for one family of linear discrete-time systems over networks with packet loss, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, the dynamic model description studied is given, which, if the packet dropout is assumed to be a discrete-time homogenous Markov process, the class of discrete-time linear systems with packet loss can be regarded as Markovian jump systems. Based on Lyapunov function approach, sufficient conditions are established for the resulting closed-loop discrete-time system with Markovian jumps to be stochasticℋ∞finite-time boundedness and then state feedback controllers are designed to guarantee stochasticℋ∞finite-time stabilization of the class of stochastic systems. The stochasticℋ∞finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the robust stochastic stabilization of the class of linear systems with packet loss. Finally, simulation examples are presented to illustrate the validity of the developed scheme.
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Polyakova, A. Yu. "Feat ures of continuing formati on of stochastic cult ure of schoolchildren in the conditions of dista nce learning." Informatics in school, no. 6 (September 25, 2021): 39–48. http://dx.doi.org/10.32517/2221-1993-2021-20-6-39-48.

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The article describes the essence of continuity in the formation of a stochastic culture of students in the conditions of distance learning. The author’s definition of the concept “continuity in the formation of stochastic culture of students of a general education school in the conditions of distance learning” is given. There are the basic conditions of a teacher’s possession of the highest level of stochastic culture, due to which the formation of an integral personal quality, which is a generalized indicator of stochastic competence, takes place in schoolchildren. Modern information and communication technologies used in a series of developed distance classes in statistics, combinatorics and probability theory for grade 11 students are proposed. These ICT contribute to the successive formation of elements of stochastic culture in the conditions of distance learning. The article emphasizes that the use of ICT in teaching stochastics is an effective methodological tool, through which significant results can be achieved in the educational process.
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Hu, Peng, and Chengming Huang. "The StochasticΘ-Method for Nonlinear Stochastic Volterra Integro-Differential Equations." Abstract and Applied Analysis 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/583930.

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The stochasticΘ-method is extended to solve nonlinear stochastic Volterra integro-differential equations. The mean-square convergence and asymptotic stability of the method are studied. First, we prove that the stochasticΘ-method is convergent of order1/2in mean-square sense for such equations. Then, a sufficient condition for mean-square exponential stability of the true solution is given. Under this condition, it is shown that the stochasticΘ-method is mean-square asymptotically stable for every stepsize if1/2≤θ≤1and when0≤θ<1/2, the stochasticΘ-method is mean-square asymptotically stable for some small stepsizes. Finally, we validate our conclusions by numerical experiments.
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Sankar, T. S., S. A. Ramu, and R. Ganesan. "Stochastic Finite Element Analysis for High Speed Rotors." Journal of Vibration and Acoustics 115, no. 1 (January 1, 1993): 59–64. http://dx.doi.org/10.1115/1.2930315.

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The general problem of the dynamic response of highspeed rotors is considered in which certain system parameters may have a spatial stochastic variation. In particular the elastic modulus and mass density of a rotating shaft are described through one dimensional stochastic field functions so that the imperfections in manufacture and measurement can be accounted for. The stochastic finite element method is developed so that the variability of the response of the rotor can be interpreted in terms of the variation of the material property. As an illustration the whirl speed analysis is performed to determine the stochastics of whirl speeds and modes through the solution of a random eigenvalue problem associated with a non self-adjoint system. Numerical results are also presented.
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TRIPŞA, Florența-Violeta, and Ana-Maria LUCA (RȊTEA). "STOCHASTIC APPROXIMATION FOR RELIABILITY PROBLEMS." SCIENTIFIC RESEARCH AND EDUCATION IN THE AIR FORCE 18, no. 1 (June 24, 2016): 497–500. http://dx.doi.org/10.19062/2247-3173.2016.18.1.68.

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Dissertations / Theses on the topic "Stochastic"

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Abi, Jaber Eduardo. "Stochastic Invariance and Stochastic Volterra Equations." Thesis, Paris Sciences et Lettres (ComUE), 2018. http://www.theses.fr/2018PSLED025/document.

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La présente thèse traite de la théorie des équations stochastiques en dimension finie. Dans la première partie, nous dérivons des conditions géométriques nécessaires et suffisantes sur les coefficients d’une équation différentielle stochastique pour l’existence d’une solution contrainte à rester dans un domaine fermé, sous de faibles conditions de régularité sur les coefficients.Dans la seconde partie, nous abordons des problèmes d’existence et d’unicité d’équations de Volterra stochastiques de type convolutif. Ces équations sont en général non-Markoviennes. Nous établissons leur correspondance avec des équations en dimension infinie ce qui nous permet de les approximer par des équations différentielles stochastiques Markoviennes en dimension finie.Enfin, nous illustrons nos résultats par une application en finance mathématique, à savoir la modélisation de la volatilité rugueuse. En particulier, nous proposons un modèle à volatilité stochastique assurant un bon compromis entre flexibilité et tractabilité
The present thesis deals with the theory of finite dimensional stochastic equations.In the first part, we derive necessary and sufficient geometric conditions on the coefficients of a stochastic differential equation for the existence of a constrained solution, under weak regularity on the coefficients. In the second part, we tackle existence and uniqueness problems of stochastic Volterra equations of convolution type. These equations are in general non-Markovian. We establish their correspondence with infinite dimensional equations which allows us to approximate them by finite dimensional stochastic differential equations of Markovian type. Finally, we illustrate our findings with an application to mathematical finance, namely rough volatility modeling. We design a stochastic volatility model with an appealing trade-off between flexibility and tractability
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Yang, Weiye. "Stochastic analysis and stochastic PDEs on fractals." Thesis, University of Oxford, 2018. http://ora.ox.ac.uk/objects/uuid:43a7af74-c531-424a-9f3d-4277138affbb.

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Stochastic analysis on fractals is, as one might expect, a subfield of analysis on fractals. An intuitive starting point is to observe that on many fractals, one can define diffusion processes whose law is in some sense invariant with respect to the symmetries and self-similarities of the fractal. These can be interpreted as fractal-valued counterparts of standard Brownian motion on Rd. One can study these diffusions directly, for example by computing heat kernel and hitting time estimates. On the other hand, by associating the infinitesimal generator of the fractal-valued diffusion with the Laplacian on Rd, it is possible to pose stochastic partial differential equations on the fractal such as the stochastic heat equation and stochastic wave equation. In this thesis we investigate a variety of questions concerning the properties of diffusions on fractals and the parabolic and hyperbolic SPDEs associated with them. Key results include an extension of Kolmogorov's continuity theorem to stochastic processes indexed by fractals, and existence and uniqueness of solutions to parabolic SPDEs on fractals with Lipschitz data.
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Fei, Lin. "On a stochastic optimization technique : stochastic probing /." The Ohio State University, 1992. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487777901661535.

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Ozkan, Pelin. "Analysis Of Stochastic And Non-stochastic Volatility Models." Master's thesis, METU, 2004. http://etd.lib.metu.edu.tr/upload/3/12605421/index.pdf.

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Changing in variance or volatility with time can be modeled as deterministic by using autoregressive conditional heteroscedastic (ARCH) type models, or as stochastic by using stochastic volatility (SV) models. This study compares these two kinds of models which are estimated on Turkish / USA exchange rate data. First, a GARCH(1,1) model is fitted to the data by using the package E-views and then a Bayesian estimation procedure is used for estimating an appropriate SV model with the help of Ox code. In order to compare these models, the LR test statistic calculated for non-nested hypotheses is obtained.
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Yakowitz, Diana Schadl. "Two-stage stochastic linear programming: Stochastic decomposition approaches." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185342.

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Stochastic linear programming problems are linear programming problems for which one or more data elements are described by random variables. Two-stage stochastic linear programming problems are problems in which a first stage decision is made before the random variables are observed. A second stage, or recourse decision, which varies with these observations compensates for any deficiencies which result from the earlier decision. Many applications areas including water resources, industrial management, economics and finance lead to two-stage stochastic linear programs with recourse. In this dissertation, two algorithms for solving stochastic linear programming problems with recourse are developed and tested. The first is referred to as Quadratic Stochastic Decomposition (QSD). This algorithm is an enhanced version of the Stochastic Decomposition (SD) algorithm of Higle and Sen (1988). The enhancements were designed to increase the computational efficiency of the SD algorithm by introducing a quadratic proximal term in the master program objective function and altering the manner in which the recourse function approximations are updated. We show that every accumulation point of an easily identifiable subsequence of points generated by the algorithm are optimal solutions to the stochastic program with probability 1. The various combinations of the enhancements are empirically investigated in a computational experiment using operations research problems from the literature. The second algorithm is an SD based algorithm for solving a stochastic linear program in which the recourse problem appears in the constraint set. This algorithm involves the use of an exact penalty function in the master program. We find that under certain conditions every accumulation point of a sequence of points generated by the algorithm is an optimal solution to the recourse constrained stochastic program, with probability 1. This algorithm is tested on several operations research problems.
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Kůdela, Jakub. "Advanced Decomposition Methods in Stochastic Convex Optimization." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-403864.

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Při práci s úlohami stochastického programování se často setkáváme s optimalizačními problémy, které jsou příliš rozsáhlé na to, aby byly zpracovány pomocí rutinních metod matematického programování. Nicméně, v některých případech mají tyto problémy vhodnou strukturu, umožňující použití specializovaných dekompozičních metod, které lze použít při řešení rozsáhlých optimalizačních problémů. Tato práce se zabývá dvěma třídami úloh stochastického programování, které mají speciální strukturu, a to dvoustupňovými stochastickými úlohami a úlohami s pravděpodobnostním omezením, a pokročilými dekompozičními metodami, které lze použít k řešení problému v těchto dvou třídách. V práci popisujeme novou metodu pro tvorbu “warm-start” řezů pro metodu zvanou “Generalized Benders Decomposition”, která se používá při řešení dvoustupňových stochastických problémů. Pro třídu úloh s pravděpodobnostním omezením zde uvádíme originální dekompoziční metodu, kterou jsme nazvali “Pool & Discard algoritmus”. Užitečnost popsaných dekompozičních metod je ukázána na několika příkladech a inženýrských aplikacích.
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Andersson, Kristina. "Stochastic Volatility." Thesis, Uppsala University, Department of Mathematics, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-121722.

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Huang, Chueng-Chiu S. "Stochastic scheduling." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/24834.

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Dean, David Stanley. "Stochastic dynamics." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.318048.

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Vedin, Robert. "Stochastic Resonance." Thesis, KTH, Skolan för teknikvetenskap (SCI), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-193632.

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Noise is often viewed as something unfortunate and unavoidable, however with the development of Stochastic Resonance (SR) theory it has been shown to have beneficial effects in many non-linear systems. We have explored the SR phenomenon via numerical simulations of two such systems. The first one is a one-dimensional Brownian particle in a bi-stable potential and the second a simple model of a signal neuron both subject to a periodic input signal. We have investigated the system responses for different input signal frequencies and noise levels in order to determine both an optimal noise level and any dependencies upon the input signal frequency.
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Books on the topic "Stochastic"

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Truman, Aubrey, and Ian M. Davies, eds. Stochastic Mechanics and Stochastic Processes. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0077911.

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1975-, McDonnell Mark D., ed. Stochastic resonance: From suprathreshold stochastic resonance to stochastic signal quantization. New York: Cambridge University Press, 2008.

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Yin, George, and Thaleia Zariphopoulou, eds. Stochastic Analysis, Filtering, and Stochastic Optimization. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-98519-6.

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Liu, Shu-Jun, and Miroslav Krstic. Stochastic Averaging and Stochastic Extremum Seeking. London: Springer London, 2012. http://dx.doi.org/10.1007/978-1-4471-4087-0.

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Kunita, Hiroshi. Stochastic flows and stochastic differential equations. Cambridge: Cambridge UniversityPress, 1990.

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Liu, Shu-Jun. Stochastic Averaging and Stochastic Extremum Seeking. London: Springer London, 2012.

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Kunita, H. Stochastic flows and stochastic differential equations. Cambridge: Cambridge University Press, 1990.

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Takahashi, Makoto, Yasuhiro Omori, and Toshiaki Watanabe. Stochastic Volatility and Realized Stochastic Volatility Models. Singapore: Springer Nature Singapore, 2023. http://dx.doi.org/10.1007/978-981-99-0935-3.

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1950-, Schimansky-Geier Lutz, Pöschel Thorsten 1963-, and Ebeling Werner 1936-, eds. Stochastic dynamics. Berlin: Springer, 1997.

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Stochastic simulation. New York: Wiley, 1987.

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Book chapters on the topic "Stochastic"

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Chang, Cheng-Shang, J. George Shanthikumar, and David D. Yao. "Stochastic Convexity and Stochastic Majorization." In Stochastic Modeling and Analysis of Manufacturing Systems, 189–231. New York, NY: Springer New York, 1994. http://dx.doi.org/10.1007/978-1-4612-2670-3_5.

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Iacus, Stefano M. "Stochastic Processes and Stochastic Differential Equations." In Springer Series in Statistics, 1–59. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-75839-8_1.

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Doleans–Dade, C. "Stochastic Processes and Stochastic Differential Equations." In Stochastic Differential Equations, 5–73. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-11079-5_1.

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Kunita, Hiroshi. "Stochastic Differential Equations and Stochastic Flows." In Stochastic Flows and Jump-Diffusions, 77–124. Singapore: Springer Singapore, 2019. http://dx.doi.org/10.1007/978-981-13-3801-4_3.

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Tallón-Ballesteros, Antonio J., Luís Correia, and Sung-Bae Cho. "Stochastic and Non-Stochastic Feature Selection." In Lecture Notes in Computer Science, 592–98. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-68935-7_64.

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Pekergin, Nihal, and Sana Younès. "Stochastic Model Checking with Stochastic Comparison." In Lecture Notes in Computer Science, 109–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11549970_9.

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Wong, Eugene, and Bruce Hajek. "Stochastic Integrals and Stochastic Differential Equations." In Springer Texts in Electrical Engineering, 139–79. New York, NY: Springer New York, 1985. http://dx.doi.org/10.1007/978-1-4612-5060-9_4.

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Hazareesingh, L., and D. Kannan. "Stochastic product integration and stochastic equations." In Lecture Notes in Mathematics, 72–120. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/bfb0072884.

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Wiart, Joe. "Stochastic Dosimetry." In Radio-Frequency Human Exposure Assessment, 119–55. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2016. http://dx.doi.org/10.1002/9781119285137.ch3.

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Aksamit, Anna, and Monique Jeanblanc. "Stochastic Processes." In SpringerBriefs in Quantitative Finance, 1–27. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-41255-9_1.

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Conference papers on the topic "Stochastic"

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Miękisz, Jacek. "Stochastic stability in spatial games." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-15.

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Mobilia, Mauro, Ivan T. Georgiev, and Uwe C. Täuber. "Spatial stochastic predator-prey models." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-16.

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Lipowsky, Reinhard, and Steffen Liepelt. "Molecular motors and stochastic networks." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-9.

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Bahuleyan, Hareesh, Lili Mou, Hao Zhou, and Olga Vechtomova. "Stochastic." In Proceedings of the 2019 Conference of the North. Stroudsburg, PA, USA: Association for Computational Linguistics, 2019. http://dx.doi.org/10.18653/v1/n19-1411.

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Stocks, N. G. "Suprathreshold stochastic resonance." In Stochastic and chaotic dynamics in the lakes. AIP, 2000. http://dx.doi.org/10.1063/1.1302415.

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Carlon, Enrico. "Thermodynamics of DNA microarrays." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-13.

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Claussen, Jens Christian. "Discrete stochastic processes, replicator and Fokker-Planck equations of coevolutionary dynamics in finite and infinite populations." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-1.

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Szabó, György. "Spreading mechanisms of cooperation for the evolutionary Prisoner's Dilemma games." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-10.

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Argasiński, Krzysztof. "Problems with classical models of sex-ratio evolution." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-11.

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Bońkowska, Katarzyna, Przemysław Biecek, Agnieszka Łaszkiewicz, and Stanisław Cebrat. "Relationship between the selection pressure and the rate of mutation accumulation." In Stochastic Models in Biological Sciences. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc80-0-12.

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Reports on the topic "Stochastic"

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Boehm, Albert R. Stochastic Indexing. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada283143.

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Boehm, Albert R. Stochastic Indexing. Fort Belvoir, VA: Defense Technical Information Center, January 1994. http://dx.doi.org/10.21236/ada283272.

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Platzer, Andre. Stochastic Differential Dynamic Logic for Stochastic Hybrid Programs. Fort Belvoir, VA: Defense Technical Information Center, April 2011. http://dx.doi.org/10.21236/ada543485.

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Cormican, Kelly J., David P. Morton, and R. K. Wood. Stochastic Network Interdiction. Fort Belvoir, VA: Defense Technical Information Center, April 1998. http://dx.doi.org/10.21236/ada491085.

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Beran, Philip S., Ned J. Lindsley, Jose Camberos, and Mohammad Kurdi. Stochastic Nonlinear Aeroelasticity. Fort Belvoir, VA: Defense Technical Information Center, January 2009. http://dx.doi.org/10.21236/ada494780.

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Turalska, M., and B. J. West. Fractional Stochastic Individuals. Fort Belvoir, VA: Defense Technical Information Center, April 2013. http://dx.doi.org/10.21236/ad1003075.

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Perez-Abreu, Victor. Product Stochastic Measures. Fort Belvoir, VA: Defense Technical Information Center, October 1985. http://dx.doi.org/10.21236/ada162833.

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X. Frank Xu. Numerical Stochastic Homogenization Method and Multiscale Stochastic Finite Element Method - A Paradigm for Multiscale Computation of Stochastic PDEs. Office of Scientific and Technical Information (OSTI), March 2010. http://dx.doi.org/10.2172/1036255.

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Evans, George, Seppo Honkapohja, and Noah Williams. Generalized Stochastic Gradient Learning. Cambridge, MA: National Bureau of Economic Research, October 2005. http://dx.doi.org/10.3386/t0317.

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HOLM, D. D., A. ACEVES, J. S. ALLEN, and ET AL. APPLIED NONLINEAR STOCHASTIC DYNAMICS. Office of Scientific and Technical Information (OSTI), November 1999. http://dx.doi.org/10.2172/785030.

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