Probability structure preserving and absolute continuity
The probability structure preserving mapping (PSPM) in the sense that \( V(F+G)= V(F)+V(G), V(FG)= V(F)V(G), E[F] = {\tilde E}[V(F)]\) for all elements \(F\) and \(G\) of the space \(\varepsilon\) of finite linear combinations of the exponential functionals defined from an abstract Wiener space together with the corresponding expectation \(E\) (respectively, \(V(F) \in \tilde {\varepsilon}\) with \( \tilde E\)) is introduced similarly to a correspondence introduced in a previous article of the author and \textit{P. A. Meyer} [in: Stochastic processes, 141-147 (1993; Zbl 0798.60057)] but a similar role is played by multiple Itô type integrals. A particular PSPM between Brownian motion and fractional Brownian motion (FBM) with Hurst parameter \(H\) is established to define stochastic integral for FBM and to prove a Girsanov type theorem on absolute continuity for FBM.
probability structure preserving mapping
scientific article; zbMATH DE number 1783425