Stochastic Calculus for Fractional Brownian Motion and Related Processes
Authors: Mishura, Yuliya
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- About this book
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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 (6 chapters)
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Wiener Integration with Respect to Fractional Brownian Motion
Pages 1-121
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Stochastic Integration with Respect to fBm and Related Topics
Pages 123-196
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Stochastic Differential Equations Involving Fractional Brownian Motion
Pages 197-290
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Filtering in Systems with Fractional Brownian Noise
Pages 291-299
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Financial Applications of Fractional Brownian Motion
Pages 301-326
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Table of contents (6 chapters)
- Download Preface 1 PDF (198.8 KB)
- Download Sample pages 1 PDF (807.3 KB)
- Download Table of contents PDF (154 KB)
- Yuliya Mishura
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Stochastic Calculus for Fractional Brownian Motion and Related Processes
- Authors
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- Yuliya Mishura
- Series Title
- Lecture Notes in Mathematics
- Series Volume
- 1929
- Copyright
- 2008
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-540-75873-0
- DOI
- 10.1007/978-3-540-75873-0
- Softcover ISBN
- 978-3-540-75872-3
- Series ISSN
- 0075-8434
- Edition Number
- 1
- Number of Pages
- XVIII, 398
- Topics
