Integral Transformations and Anticipative Calculus for Fractional Brownian Motions (Memoirs of the American Mathematical Society No. 175)
By: Yaozhong Hu (author)Paperback
1 - 2 weeks availability
This paper studies two types of integral transformation associated with fractional Brownian motion. They are applied to construct approximation schemes for fractional Brownian motion by polygonal approximation of standard Brownian motion. This approximation is the best in the sense that it minimizes the mean square error. The rate of convergence for this approximation is obtained. The integral transformations are combined with the idea of probability structure preserving mapping introduced in  and are applied to develop a stochastic calculus for fractional Brownian motions of all Hurst parameter $H\in (0, 1)$.In particular we obtain Radon-Nikodym derivative of nonlinear (random) translation of fractional Brownian motion over finite interval, extending the results of  to general case. We obtain an integration by parts formula for general stochastic integral and an Ito type formula for some stochastic integral. The conditioning, Clark derivative, continuity of stochastic integral are also studied. As an application we study a linear quadratic control problem, where the system is driven by fractional Brownian motion.
Introduction Representations Induced transformation I Approximation Induced transformation II Stochastic calculus of variation Stochastic integration Nonlinear translation (Absolute continuity) Conditional expectation Integration by parts Composition (Ito formula) Clark type representation Continuation Stochastic control Appendix Bibliography.
Number Of Pages:
- ID: 9780821837047
- Saver Delivery: Yes
- 1st Class Delivery: Yes
- Courier Delivery: Yes
- Store Delivery: Yes
Prices are for internet purchases only. Prices and availability in WHSmith Stores may vary significantly
© Copyright 2013 - 2016 WHSmith and its suppliers.
WHSmith High Street Limited Greenbridge Road, Swindon, Wiltshire, United Kingdom, SN3 3LD, VAT GB238 5548 36