Asymptotic Methods in Stochastics

Asymptotic Methods in Stochastics
Title Asymptotic Methods in Stochastics PDF eBook
Author Lajos Horvath and Barbara Szyszkowicz
Publisher American Mathematical Soc.
Pages 552
Release
Genre Asymptotic expansions
ISBN 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
Title Asymptotic Methods in the Theory of Stochastic Differential Equations PDF eBook
Author A. V. Skorokhod
Publisher American Mathematical Soc.
Pages 362
Release 2009-01-07
Genre Mathematics
ISBN 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

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
Title Asymptotic Methods for the Fokker-Planck Equation and the Exit Problem in Applications PDF eBook
Author Johan Grasman
Publisher Springer Science & Business Media
Pages 242
Release 1999-03-08
Genre Mathematics
ISBN 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.

Stochastic Geometry, Spatial Statistics and Random Fields

Stochastic Geometry, Spatial Statistics and Random Fields
Title Stochastic Geometry, Spatial Statistics and Random Fields PDF eBook
Author Evgeny Spodarev
Publisher Springer
Pages 470
Release 2013-02-11
Genre Mathematics
ISBN 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.

Theory and Applications of Stochastic Processes

Theory and Applications of Stochastic Processes
Title Theory and Applications of Stochastic Processes PDF eBook
Author Zeev Schuss
Publisher Springer Science & Business Media
Pages 486
Release 2009-12-09
Genre Mathematics
ISBN 1441916059

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Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular biophysics, communications theory and many more. Many books, reviews and research articles have been published on this topic, from the purely mathematical to the most practical. This book offers an analytical approach to stochastic processes that are most common in the physical and life sciences, as well as in optimal control and in the theory of filltering of signals from noisy measurements. Its aim is to make probability theory in function space readily accessible to scientists trained in the traditional methods of applied mathematics, such as integral, ordinary, and partial differential equations and asymptotic methods, rather than in probability and measure theory.

Asymptotic Laws and Methods in Stochastics

Asymptotic Laws and Methods in Stochastics
Title Asymptotic Laws and Methods in Stochastics PDF eBook
Author Donald Dawson
Publisher Springer
Pages 401
Release 2015-11-12
Genre Mathematics
ISBN 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 Theory of Statistical Inference for Time Series

Asymptotic Theory of Statistical Inference for Time Series
Title Asymptotic Theory of Statistical Inference for Time Series PDF eBook
Author Masanobu Taniguchi
Publisher Springer
Pages 0
Release 2012-10-23
Genre Mathematics
ISBN 9781461270287

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The primary aim of this book is to provide modern statistical techniques and theory for stochastic processes. The stochastic processes mentioned here are not restricted to the usual AR, MA, and ARMA processes. A wide variety of stochastic processes, including non-Gaussian linear processes, long-memory processes, nonlinear processes, non-ergodic processes and diffusion processes are described. The authors discuss estimation and testing theory and many other relevant statistical methods and techniques.