Stochastic calculus for fractional Brownian motion and related processes

✍ Scribed by Yuliya S. Mishura (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2008
• Tongue: English
• Leaves: 411
• Series: Lecture Notes in Mathematics 1929
• Edition: 1
• Category: Library

✦ Synopsis

The theory of fractional Brownian motion and other long-memory processes are addressed in this volume. Interesting topics for PhD students and specialists in probability theory, stochastic analysis and financial mathematics demonstrate the modern level of this field. Among these are results about Levy characterization of fractional Brownian motion, maximal moment inequalities for Wiener integrals including the values 0<H<1/2 of Hurst index, the conditions of existence and uniqueness of solutions to SDE involving additive Wiener integrals, and of solutions of the mixed Brownian—fractional Brownian SDE. The author develops optimal filtering of mixed models including linear case, and studies financial applications and statistical inference with hypotheses testing and parameter estimation. She proves that the market with stock guided by the mixed model is arbitrage-free without any restriction on the dependence of the components and deduces different forms of the Black-Scholes equation for fractional market.

✦ Table of Contents

Front Matter....Pages I-XVII
Wiener Integration with Respect to Fractional Brownian Motion....Pages 1-121
Stochastic Integration with Respect to fBm and Related Topics....Pages 123-196
Stochastic Differential Equations Involving Fractional Brownian Motion....Pages 197-290
Filtering in Systems with Fractional Brownian Noise....Pages 291-299
Financial Applications of Fractional Brownian Motion....Pages 301-326
Statistical Inference with Fractional Brownian Motion....Pages 327-362
Back Matter....Pages 363-393

✦ Subjects

Probability Theory and Stochastic Processes; Game Theory, Economics, Social and Behav. Sciences