Brownian Motion: A Guide to Random Processes and Stochastic Calculus

René L. Schilling

Published by De Gruyter 2021

Brownian Motion

A Guide to Random Processes and Stochastic Calculus

René L. Schilling
With contributions by: Björn Böttcher

In the series De Gruyter Textbook

https://doi.org/10.1515/9783110741278

Overview
Contents

About this book

Stochastic processes occur everywhere in the sciences, economics and engineering, and they need to be understood by (applied) mathematicians, engineers and scientists alike. This book gives a gentle introduction to Brownian motion and stochastic processes, in general. Brownian motion plays a special role, since it shaped the whole subject, displays most random phenomena while being still easy to treat, and is used in many real-life models. Im this new edition, much material is added, and there are new chapters on ''Wiener Chaos and Iterated Itô Integrals'' and ''Brownian Local Times''.

3rd revised and extended edition

More than 200 exercises

Solutions included

For mathematicians, economists, engineers and scientists

Author / Editor information

René L. Schilling, Technical University Dresden, Germany.

Topics

Frontmatter Publicly Available Download PDF	I
Preface Publicly Available Download PDF	V
Contents Publicly Available Download PDF	VII
Dependence chart Publicly Available Download PDF	XI
1 Robert Brown’s new thing Requires Authentication Unlicensed Licensed Download PDF	1
2 Brownian motion as a Gaussian process Requires Authentication Unlicensed Licensed Download PDF	7
3 Constructions of Brownian motion Requires Authentication Unlicensed Licensed Download PDF	20
4 The canonical model Requires Authentication Unlicensed Licensed Download PDF	39
5 Brownian motion as a martingale Requires Authentication Unlicensed Licensed Download PDF	48
6 Brownian motion as a Markov process Requires Authentication Unlicensed Licensed Download PDF	62
7 Brownian motion and transition semigroups Requires Authentication Unlicensed Licensed Download PDF	87
8 The PDE connection Requires Authentication Unlicensed Licensed Download PDF	124
9 The variation of Brownian paths Requires Authentication Unlicensed Licensed Download PDF	152
10 Regularity of Brownian paths Requires Authentication Unlicensed Licensed Download PDF	167
11 Brownian motion as a random fractal Requires Authentication Unlicensed Licensed Download PDF	177
12 The growth of Brownian paths Requires Authentication Unlicensed Licensed Download PDF	198
13 Strassen’s functional law of the iterated logarithm Requires Authentication Unlicensed Licensed Download PDF	212
14 Skorokhod representation Requires Authentication Unlicensed Licensed Download PDF	232
15 Stochastic integrals: L²-Theory Requires Authentication Unlicensed Licensed Download PDF	244
16 Stochastic integrals: localization Requires Authentication Unlicensed Licensed Download PDF	273
17 Stochastic integrals: martingale drivers Requires Authentication Unlicensed Licensed Download PDF	283
18 Itô’s formula Requires Authentication Unlicensed Licensed Download PDF	297
19 Applications of Itô’s formula Requires Authentication Unlicensed Licensed Download PDF	317
20 Wiener Chaos and iterated Wiener–Itô integrals Requires Authentication Unlicensed Licensed Download PDF	361
21 Stochastic differential equations Requires Authentication Unlicensed Licensed Download PDF	383
22 Stratonovich’s stochastic calculus Requires Authentication Unlicensed Licensed Download PDF	417
23 On diffusions Requires Authentication Unlicensed Licensed Download PDF	427
24 Simulation of Brownian motion by Björn Böttcher Requires Authentication Unlicensed Licensed Download PDF	460
A Appendix Requires Authentication Unlicensed Licensed Download PDF	474
Bibliography Requires Authentication Unlicensed Licensed Download PDF	503
Index Requires Authentication Unlicensed Licensed Download PDF	514

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 3rd Edition
Audience: Students in Mathematics and Finance, Physics, Economics, Engineering; Professionals in Finance and Industry.
Pages
- Front matter: 14
- Main content: 519
Illustrations
- Illustrations: 30
- Tables: 3
Keywords: Brownsche Bewegung; Stochastische Prozesse; Pfadeigenschaften; Finanzmathematik

eBook

Published: September 7, 2021
ISBN: 9783110741278

Paperback

Published: September 7, 2021
ISBN: 9783110741254