Probability and Stochastics

by Çinlar, Erhan

Type Book

Rate 0.0 /5

Details

Files

Reviews

Download

Title Statements

Full title :Probability and Stochastics.

Summary

This text is an introduction to the modern theory and applications of probability and stochastics. The style and coverage is geared towards the theory of stochastic processes, but with some attention to the applications. In many instances the gist of the problem is introduced in practical, everyday language and then is made precise in mathematical form. The first four chapters are on probability theory: measure and integration, probability spaces, conditional expectations, and the classical limit theorems. There follows chapters on martingales, Poisson random measures, Levy Processes, Brownian motion, and Markov Processes. Special attention is paid to Poisson random measures and their roles in regulating the excursions of Brownian motion and the jumps of Levy and Markov processes. Each chapter has a large number of varied examples and exercises. The book is based on the author's lecture notes in courses offered over the years at Princeton University. These courses attracted graduate students from engineering, economics, physics, computer sciences, and mathematics. Erhan Çinlar has received many awards for excellence in teaching, including the President's Award for Distinguished Teaching at Princeton University. His research interests include theories of Markov processes, point processes, stochastic calculus, and stochastic flows. The book is full of insights and observations that only a lifetime researcher in probability can have, all told in a lucid yet precise style.

Edition Statements

Publication Date:2011.
Edition:2nd ed

Publication Statements

Publisher(s):Springer New York
Place of Publication:New York, NY
Language:eng
Publication Date:2011.

The Physical Object

Description:1 online resource (566 pages)

Edition Identifiers

ISBN:0387878580, 9780387878584
DOI:10.1007/978-0-387-87859-1
oclc:ocn990655484
LC Classification:QA273.C56 2011eb
Dewey Decimal:616.3623

""Probability and Stochastics ""; ""Preface""; ""Frequently Used Notation""; ""Contents""; ""Chapter I: Measure and Integration ""; ""1 Measurable Spaces""; ""2 Measurable Functions""; ""3 Measures""; ""4 Integration""; ""5 Transforms and Indefinite Integrals""; ""6 Kernels and Product Spaces""; ""Chapter II: Probability Spaces ""; ""1 Probability Spaces and Random Variables""; ""2 Expectations""; ""3 Lp-spaces and Uniform Integrability""; ""4 Information and Determinability""; ""5 Independence""; ""Chapter III: Convergence ""; ""1 Convergence of Real Sequences""

""2 Almost Sure Convergence""""3 Convergence in Probability""; ""4 Convergence in Lp""; ""5 Weak Convergence""; ""6 Laws of Large Numbers""; ""7 Convergence of Series""; ""8 Central Limits""; ""Chapter IV: Conditioning ""; ""1 Conditional Expectations""; ""2 Conditional Probabilities and Distributions""; ""3 Conditional Independence""; ""4 Construction of Probability Spaces""; ""5 Special Constructions""; ""Chapter V: Martingales and Stochastics ""; ""1 Filtrations and Stopping Times""; ""2 Martingales""; ""3 Martingale Transformations and Maxima""; ""4 Martingale Convergence""

""5 Martingales in Continuous Time""""6 Ma…