Absolute Continuity Under Time Shift of Trajectories and Related Stochastic Calculus

ISBN-13: 9781470426033 / Angielski

Jorg-Uwe Lobus

Opis

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?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.

Spis treści

• Introduction, Basic objects, and main result
• Flows and logarithmic derivative relative to $X$ under orthogonal projection
• The density formula
• Partial integration
• Relative compactness of particle systems
• Appendix A. Basic Malliavin calculus for Brownian motion with random initial data
• References
• Index.