Absolute continuity of probability laws of Wiener functionals

Probability Structure Preserving and Absolute Continuity ✩

– The concept of probability structure preserving mapping is introduced. The idea is applied to define stochastic integral for fractional Brownian motion (fBm) and to obtain an anticipative Girsanov theorem for fBm.  2002 Éditions scientifiques et médicales Elsevier SAS AMS classification: 60H05; 60H07; 60H15; 60B11; 28B20

Absolute Continuity between the Wiener and Stationary Gaussian Measures

It is known that the entropy distance between two Gaussian measures is finite if, and only if, they are absolutely continuous with respect to one another. Shepp [5] characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the spe...

Absolute Continuity and Singularity of Probability Measures in Functional Spaces

Weak Approximations for Wiener Functionals

Abstract. In this paper we introduce a simple space-filtration discretization scheme on Wiener space which allows us to study weak decompositions of a large class of Wiener functionals. We show that any Wiener functional has an underlying robust semimartingale skeleton which under mild conditions converges to it. The approximation is given in terms of discrete-jumping filtrations which allow us...

analysis of ruin probability for insurance companies using markov chain

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