Stochastic Calculus for Fractional Brownian Motion and Related Processes / by Yuliya S. Mishura.

Format:

Book

Author/Creator:

Mishura, I︠U︡lii︠a︡ S., author.

Contributor:

SpringerLink (Online service)

Series:

Lecture Notes in Mathematics, 0075-8434 ; 1929.

Lecture Notes in Mathematics, 0075-8434 ; 1929

Language:

English

Subjects (All):

Distribution (Probability theory).

Mathematics.

Probability Theory and Stochastic Processes.

Game Theory, Economics, Social and Behav. Sciences.

Local Subjects:

Probability Theory and Stochastic Processes.

Game Theory, Economics, Social and Behav. Sciences.

Physical Description:

1 online resource (XVIII, 398 pages).

Contained In:

Springer eBooks

Place of Publication:

Berlin, Heidelberg : Springer Berlin Heidelberg, 2008.

System Details:

text file PDF

Summary:

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.

Contents:

Wiener Integration with Respect to Fractional Brownian Motion

Stochastic Integration with Respect to fBm and Related Topics

Stochastic Differential Equations Involving Fractional Brownian Motion

Filtering in Systems with Fractional Brownian Noise

Financial Applications of Fractional Brownian Motion

Statistical Inference with Fractional Brownian Motion.

Other Format:

Printed edition:

ISBN:

9783540758730

Access Restriction:

Restricted for use by site license.