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Stochastic Calculus for Fractional Brownian Motion and Related Processes

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1929)

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About this book

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.

Keywords

  • Maxima
  • Probability theory
  • Stochastic calculus
  • financial markets
  • fractional Brownian motion
  • statistical inference
  • stochastic differential equations
  • stochastic integration

Authors and Affiliations

  • Department of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Kyiv, Ukraine

    Yuliya S. Mishura

Bibliographic Information

  • Book Title: Stochastic Calculus for Fractional Brownian Motion and Related Processes

  • Authors: Yuliya S. Mishura

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-540-75873-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2008

  • Softcover ISBN: 978-3-540-75872-3Published: 30 November 2007

  • eBook ISBN: 978-3-540-75873-0Published: 12 April 2008

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XVIII, 398

  • Topics: Probability Theory, Game Theory

Buying options

eBook USD 54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 69.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions