Asymptotic Laws and Methods in Stochastics
Asymptotic Laws and Methods in Stochastics

Author: Donald Dawson

Publisher: Springer

Published: 2015-11-12

Total Pages: 401

ISBN-13: 1493930761

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This book contains articles arising from a conference in honour of mathematician-statistician Miklόs Csörgő on the occasion of his 80th birthday, held in Ottawa in July 2012. It comprises research papers and overview articles, which provide a substantial glimpse of the history and state-of-the-art of the field of asymptotic methods in probability and statistics, written by leading experts. The volume consists of twenty articles on topics on limit theorems for self-normalized processes, planar processes, the central limit theorem and laws of large numbers, change-point problems, short and long range dependent time series, applied probability and stochastic processes, and the theory and methods of statistics. It also includes Csörgő’s list of publications during more than 50 years, since 1962.

Asymptotic Methods in Stochastics
Asymptotic Methods in Stochastics

Author: M. Csörgö

Publisher: American Mathematical Soc.

Published: 2004

Total Pages: 546

ISBN-13: 0821835610

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Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Asymptotic Methods in Stochastics
Asymptotic Methods in Stochastics

Author: Lajos Horvath and Barbara Szyszkowicz

Publisher: American Mathematical Soc.

Published:

Total Pages: 552

ISBN-13: 9780821871485

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Honoring over forty years of Miklos Csorgo's work in probability and statistics, this title shows the state of the research. This book covers such topics as: path properties of stochastic processes, weak convergence of random size sums, almost sure stability of weighted maxima, and procedures for detecting changes in statistical models.

Asymptotic Methods in the Theory of Stochastic Differential Equations
Asymptotic Methods in the Theory of Stochastic Differential Equations

Author: A. V. Skorokhod

Publisher: American Mathematical Soc.

Published: 2009-01-07

Total Pages: 339

ISBN-13: 9780821846865

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Written by one of the foremost Soviet experts in the field, this book is intended for specialists in the theory of random processes and its applications. The author's 1982 monograph on stochastic differential equations, written with Iosif Ilich Gikhman, did not include a number of topics important to applications. The present work begins to fill this gap by investigating the asymptotic behavior of stochastic differential equations. The main topics are ergodic theory for Markov processes and for solutions of stochastic differential equations, stochastic differential equations containing a small parameter, and stability theory for solutions of systems of stochastic differential equations.

Asymptotic Methods in the Theory of Stochastic Differential Equations
Asymptotic Methods in the Theory of Stochastic Differential Equations

Author: A. V. Skorokhod

Publisher: American Mathematical Soc.

Published: 2009-01-07

Total Pages: 362

ISBN-13: 9780821898253

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Ergodic theorems: General ergodic theorems Densities for transition probabilities and resolvents for Markov solutions of stochastic differential equations Ergodic theorems for one-dimensional stochastic equations Ergodic theorems for solutions of stochastic equations in $R^d$ Asymptotic behavior of systems of stochastic equations containing a small parameter: Equations with a small right-hand side Processes with rapid switching Averaging over variables for systems of stochastic differential equations Stability. Linear systems: Stability of sample paths of homogeneous Markov processes Linear equations in $R^d$ and the stochastic semigroups connected with them. Stability Stability of solutions of stochastic differential equations Linear stochastic equations in Hilbert space. Stochastic semigroups. Stability: Linear equations with bounded coefficients Strong stochastic semigroups with second moments Stability Bibliography

Stochastic Geometry, Spatial Statistics and Random Fields
Stochastic Geometry, Spatial Statistics and Random Fields

Author: Evgeny Spodarev

Publisher: Springer

Published: 2013-02-11

Total Pages: 470

ISBN-13: 3642333052

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This volume provides a modern introduction to stochastic geometry, random fields and spatial statistics at a (post)graduate level. It is focused on asymptotic methods in geometric probability including weak and strong limit theorems for random spatial structures (point processes, sets, graphs, fields) with applications to statistics. Written as a contributed volume of lecture notes, it will be useful not only for students but also for lecturers and researchers interested in geometric probability and related subjects.

Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms
Asymptotic and Analytic Methods in Stochastic Evolutionary Symptoms

Author: Dmitri Koroliouk

Publisher: John Wiley & Sons

Published: 2023-07-26

Total Pages: 276

ISBN-13: 139422947X

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This book illustrates a number of asymptotic and analytic approaches applied for the study of random evolutionary systems, and considers typical problems for specific examples. In this case, constructive mathematical models of natural processes are used, which more realistically describe the trajectories of diffusion-type processes, rather than those of the Wiener process. We examine models where particles have some free distance between two consecutive collisions. At the same time, we investigate two cases: the Markov evolutionary system, where the time during which the particle moves towards some direction is distributed exponentially with intensity parameter λ; and the semi-Markov evolutionary system, with arbitrary distribution of the switching process. Thus, the models investigated here describe the motion of particles with a finite speed and the proposed random evolutionary process with characteristics of a natural physical process: free run and finite propagation speed. In the proposed models, the number of possible directions of evolution can be finite or infinite.

Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications
Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications

Author: Johan Grasman

Publisher: Springer Science & Business Media

Published: 1999-03-08

Total Pages: 242

ISBN-13: 9783540644354

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Asymptotic methods are of great importance for practical applications, especially in dealing with boundary value problems for small stochastic perturbations. This book deals with nonlinear dynamical systems perturbed by noise. It addresses problems in which noise leads to qualitative changes, escape from the attraction domain, or extinction in population dynamics. The most likely exit point and expected escape time are determined with singular perturbation methods for the corresponding Fokker-Planck equation. The authors indicate how their techniques relate to the Itô calculus applied to the Langevin equation. The book will be useful to researchers and graduate students.