Asymptotic Methods In Stochastics
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| Author | : Lajos Horvath and Barbara Szyszkowicz |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 552 |
| Release | : |
| Genre | : Asymptotic expansions |
| ISBN | : 9780821871485 |
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.
| Author | : A. V. Skorokhod |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 362 |
| Release | : 2009-01-07 |
| Genre | : Mathematics |
| ISBN | : 9780821898253 |
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
| Author | : Johan Grasman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 242 |
| Release | : 1999-03-08 |
| Genre | : Mathematics |
| ISBN | : 9783540644354 |
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.
| Author | : Dmitri Koroliouk |
| Publisher | : John Wiley & Sons |
| Total Pages | : 276 |
| Release | : 2023-07-26 |
| Genre | : Mathematics |
| ISBN | : 139422947X |
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.
| Author | : Evgeny Spodarev |
| Publisher | : Springer |
| Total Pages | : 470 |
| Release | : 2013-02-11 |
| Genre | : Mathematics |
| ISBN | : 3642333052 |
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.
| Author | : Zeev Schuss |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 486 |
| Release | : 2009-12-09 |
| Genre | : Mathematics |
| ISBN | : 1441916059 |
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.
| Author | : Anatolij V. Skorochod |
| Publisher | : Walter de Gruyter GmbH & Co KG |
| Total Pages | : 192 |
| Release | : 2019-01-14 |
| Genre | : Mathematics |
| ISBN | : 3110618168 |
No detailed description available for "Lectures on the Theory of Stochastic Processes".
| Author | : Vladimir I. Piterbarg |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 222 |
| Release | : 2012-03-28 |
| Genre | : Mathematics |
| ISBN | : 0821883313 |
This book is devoted to a systematic analysis of asymptotic behavior of distributions of various typical functionals of Gaussian random variables and fields. The text begins with an extended introduction, which explains fundamental ideas and sketches the basic methods fully presented later in the book. Good approximate formulas and sharp estimates of the remainders are obtained for a large class of Gaussian and similar processes. The author devotes special attention to the development of asymptotic analysis methods, emphasizing the method of comparison, the double-sum method and the method of moments. The author has added an extended introduction and has significantly revised the text for this translation, particularly the material on the double-sum method.
| Author | : Norbert Henze |
| Publisher | : Springer Nature |
| Total Pages | : 470 |
| Release | : |
| Genre | : |
| ISBN | : 3662689235 |
| Author | : Masanobu Taniguchi |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2012-10-23 |
| Genre | : Mathematics |
| ISBN | : 9781461270287 |
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.
