A Class of Infinitesimal Generators and Time Reversal for the Corresponding One-Dimensional Markov Processes

✍ Scribed by M. Weber

• Publisher: John Wiley and Sons
• Year: 1992
• Tongue: English
• Weight: 504 KB
• Volume: 157
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19921570106

✦ Synopsis

Abstract

A class of infinitesimal generators A of strongly continuous nonnegative contraction semigroups in a subspace of C[0, 1] is introduced. It contains the class of generators of regular gap diffusions. A construction of the Markov process X generated by A gives some stochastic interpretations of the integral term which appears in A. The infinitesimal generator of the time reversal of X (with respect to its life time) is explicitly given. It belongs to the introduced class of generators too. Thus, the considered class is invariant under this transformation. Two examples, the time reversal of gap diffusions with nonlocal boundary conditions and the time reversal of processes with Levy‐measure, complete the note.