Download or read book Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus written by Jörg-Uwe Löbus and published by . This book was released on 2017 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text is concerned with a class of two-sided stochastic processes of the form X=W+A. Here W is a two-sided Brownian motion with random initial data at time zero and A\equiv A(W) is a function of W. Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when A is a jump process. Absolute continuity of (X,P) under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, m, and on A with A_0=0 we verify \frac{P(dX_{\cdot -t})}{P(dX_\cdot)}=\frac{m(X_{-t}