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Absolute Continuity under Time Shift of Trajectories and Related Stochastic Calculus
Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
2017 (English)In: Memoirs of the American Mathematical Society, ISSN 0065-9266, E-ISSN 1947-6221, Vol. 249, no 1185, 1-135 p.Article 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. Vol. 249, no 1185, 1-135 p.
Keyword [en]
Non-linear transformation of measures, anticipative stochastic calculus, Brownian motion, jump processes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-141626DOI: 10.1090/memo/1185OAI: oai:DiVA.org:liu-141626DiVA: diva2:1146787
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).

Available from: 2017-10-04 Created: 2017-10-04 Last updated: 2017-10-04Bibliographically approved

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Löbus, Jörg-Uwe
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CiteExportLink to record
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Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf