Stochastic analysis on configuration spaces: basic ideas and recent results

Details Stochastic analysis on configuration spaces: basic ideas and recent results Stochastic analysis on configuration spaces: basic ideas and recent results

1998-03-31

arxiv.org/abs/math/9803162v1

Mathematics

Probability

Scientific paper

The purpose of this paper is to provide a both comprehensive and summarizing account on recent results about analysis and geometry on configuration spaces $\Gamma_X$ over Riemannian manifolds $X$. Particular emphasis is given to a complete description of the so--called ``lifting--procedure'', Markov resp. strong resp. $L^1$--uniqueness results, the non--conservative case, the interpretation of the constructed diffusions as solutions of the respective classical ``heuristic'' stochastic differential equations, and a self--contained presentation of a general closability result for the corresponding pre--Dirichlet forms. The latter is presented in the general case of arbitrary (not necessarily pair) potentials describing the singular interactions. A support property for the diffusions, the intrinsic metric, and a Rademacher theorem on $\Gamma_X$, recently proved, are also discussed.

Affiliated with

Also associated with

No associations

Rating

Stochastic analysis on configuration spaces: basic ideas and recent results 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 Stochastic analysis on configuration spaces: basic ideas and recent results, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stochastic analysis on configuration spaces: basic ideas and recent results will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-309670