Stochastic-Process Limits
Title | Stochastic-Process Limits PDF eBook |
Author | Ward Whitt |
Publisher | Springer Science & Business Media |
Pages | 616 |
Release | 2006-04-11 |
Genre | Mathematics |
ISBN | 0387217487 |
From the reviews: "The material is self-contained, but it is technical and a solid foundation in probability and queuing theory is beneficial to prospective readers. [... It] is intended to be accessible to those with less background. This book is a must to researchers and graduate students interested in these areas." ISI Short Book Reviews
Limit Theorems for Stochastic Processes
Title | Limit Theorems for Stochastic Processes PDF eBook |
Author | Jean Jacod |
Publisher | Springer Science & Business Media |
Pages | 620 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 3662025140 |
Initially the theory of convergence in law of stochastic processes was developed quite independently from the theory of martingales, semimartingales and stochastic integrals. Apart from a few exceptions essentially concerning diffusion processes, it is only recently that the relation between the two theories has been thoroughly studied. The authors of this Grundlehren volume, two of the international leaders in the field, propose a systematic exposition of convergence in law for stochastic processes, from the point of view of semimartingale theory, with emphasis on results that are useful for mathematical theory and mathematical statistics. This leads them to develop in detail some particularly useful parts of the general theory of stochastic processes, such as martingale problems, and absolute continuity or contiguity results. The book contains an elementary introduction to the main topics: theory of martingales and stochastic integrales, Skorokhod topology, etc., as well as a large number of results which have never appeared in book form, and some entirely new results. It should be useful to the professional probabilist or mathematical statistician, and of interest also to graduate students.
Limit Theorems for Randomly Stopped Stochastic Processes
Title | Limit Theorems for Randomly Stopped Stochastic Processes PDF eBook |
Author | Dmitrii S. Silvestrov |
Publisher | Springer Science & Business Media |
Pages | 408 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 0857293907 |
This volume is the first to present a state-of-the-art overview of this field, with many results published for the first time. It covers the general conditions as well as the basic applications of the theory, and it covers and demystifies the vast and technically demanding Russian literature in detail. Its coverage is thorough, streamlined and arranged according to difficulty.
Limit Theorems for Randomly Stopped Stochastic Processes
Title | Limit Theorems for Randomly Stopped Stochastic Processes PDF eBook |
Author | Dimitri Silvestrov |
Publisher | |
Pages | 416 |
Release | 2014-01-15 |
Genre | |
ISBN | 9780857293916 |
Convergence of Stochastic Processes
Title | Convergence of Stochastic Processes PDF eBook |
Author | D. Pollard |
Publisher | David Pollard |
Pages | 223 |
Release | 1984-10-08 |
Genre | Mathematics |
ISBN | 0387909907 |
Functionals on stochastic processes; Uniform convergence of empirical measures; Convergence in distribution in euclidean spaces; Convergence in distribution in metric spaces; The uniform metric on space of cadlag functions; The skorohod metric on D [0, oo); Central limit teorems; Martingales.
Scaling Limits of Stochastic Processes
Title | Scaling Limits of Stochastic Processes PDF eBook |
Author | Amanda Georgina Turner |
Publisher | |
Pages | |
Release | 2007 |
Genre | |
ISBN |
A First Look At Stochastic Processes
Title | A First Look At Stochastic Processes PDF eBook |
Author | Jeffrey S Rosenthal |
Publisher | World Scientific |
Pages | 213 |
Release | 2019-09-26 |
Genre | Mathematics |
ISBN | 9811207925 |
This textbook introduces the theory of stochastic processes, that is, randomness which proceeds in time. Using concrete examples like repeated gambling and jumping frogs, it presents fundamental mathematical results through simple, clear, logical theorems and examples. It covers in detail such essential material as Markov chain recurrence criteria, the Markov chain convergence theorem, and optional stopping theorems for martingales. The final chapter provides a brief introduction to Brownian motion, Markov processes in continuous time and space, Poisson processes, and renewal theory.Interspersed throughout are applications to such topics as gambler's ruin probabilities, random walks on graphs, sequence waiting times, branching processes, stock option pricing, and Markov Chain Monte Carlo (MCMC) algorithms.The focus is always on making the theory as well-motivated and accessible as possible, to allow students and readers to learn this fascinating subject as easily and painlessly as possible.