Open this publication in new window or tab >>2017 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 249, no 1185, p. 1-135Article in journal (Refereed) Published
Abstract [en]
The text is concerned with a class of two-sided stochastic processes of the form . Here is a two-sided Brownian motion with random initial data at time zero and is a function of . Elements of the related stochastic calculus are introduced. In particular, the calculus is adjusted to the case when is a jump process. Absolute continuity of under time shift of trajectories is investigated. For example under various conditions on the initial density with respect to the Lebesgue measure, , and on with we verifya.e. where the product is taken over all coordinates. Here is the divergence of with respect to the initial position. Crucial for this is the temporal homogeneity of in the sense that , , where is the trajectory taking the constant value .By means of such a density, partial integration relative to a generator type operator of the process is established. Relative compactness of sequences of such processes is established.
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2017
Keywords
Non-linear transformation of measures, anticipative stochastic calculus, Brownian motion, jump processes
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-141626 (URN)10.1090/memo/1185 (DOI)000412226700001 ()
Note
Chapters
Chapter 1. Introduction, Basic Objects, and Main Result
Chapter 2. Flows and Logarithmic Derivative Relative to X" role="presentation">X under Orthogonal Projection
Chapter 3. The Density Formula
Chapter 4. Partial Integration
Chapter 5. Relative Compactness of Particle Systems
Appendix A. Basic Malliavin Calculus for Brownian Motion with Random Initial Data
ISBN: 978-1-4704-2603-3 (print); 978-1-4704-4137-1 (online).
2017-10-042017-10-042018-03-16Bibliographically approved