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QUASI-INVARIANCE FORMULAS FOR COMPONENTS OF QUANTUM LÉVY PROCESSES.
- Source :
-
Infinite Dimensional Analysis, Quantum Probability & Related Topics . Mar2004, Vol. 7 Issue 1, p131-145. 15p. - Publication Year :
- 2004
-
Abstract
- A general method for deriving Girsanov or quasi-invariance formulas for classical stochastic processes with independent increments obtained as components of Lévy processes on real Lie algebras is presented. Letting a unitary operator arising from the associated factorizable current representation act on an appropriate commutative subalgebra, a second commutative subalgebra is obtained. Under certain conditions the two commutative subalgebras lead to two classical processes such that the law of the second process is absolutely continuous w.r.t. to the first. Examples include the Girsanov formula for Brownian motion as well as quasi-invariance formulas for the Poisson process, the Gamma process,[sup 15,16] and the Meixner process. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02190257
- Volume :
- 7
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Infinite Dimensional Analysis, Quantum Probability & Related Topics
- Publication Type :
- Academic Journal
- Accession number :
- 12538977
- Full Text :
- https://doi.org/10.1142/S0219025704001499