Superposition rules and stochastic Lie-Scheffers systems

Details Superposition rules and stochastic Lie-Scheffers systems Superposition rules and stochastic Lie-Scheffers systems

2008-03-05

arxiv.org/abs/0803.0600v1

Mathematics

Probability

Scientific paper

This paper proves a version for stochastic differential equations of the Lie-Scheffers Theorem. This result characterizes the existence of nonlinear superposition rules for the general solution of those equations in terms of the involution properties of the distribution generated by the vector fields that define it. When stated in the particular case of standard deterministic systems, our main theorem improves various aspects of the classical Lie-Scheffers result. We show that the stochastic analog of the classical Lie-Scheffers systems can be reduced to the study of Lie group valued stochastic Lie-Scheffers systems; those systems, as well as those taking values in homogeneous spaces are studied in detail. The developments of the paper are illustrated with several examples.

Affiliated with

Also associated with

No associations

Rating

Superposition rules and stochastic Lie-Scheffers systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Superposition rules and stochastic Lie-Scheffers systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Superposition rules and stochastic Lie-Scheffers systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-160753