Abstract
In this article, we consider a white noise calculus for fractional Brownian motion with values in a separable Hilbert space, whereby the covariance operator Q is a kernel operator (Q-fractional Brownian motion). We introduce a fractional exponential, Q-fractional test function space , and a corresponding distribution space and the Q-fractional version of the Wick product, so that we can define a stochastic integral with respect to a fractional white noise process. Furthermore, a Q-fractional version of the Girsanov formula and a Q-fractional version of the Clark–Haussmann–Ocone theorem are proved. As applications, the solution for a stochastic evolution equation driven by fractional Brownian motion and an infinite-dimensional fractional Black–Scholes market are discussed.
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