Self-repelling diffusions via an infinite dimensional approach
arXiv:1408.6397 · doi:10.1007/s40072-015-0059-5
Abstract
In the present work we study self-interacting diffusions following an infinite dimensional approach. First we prove existence and uniqueness of a solution with Markov property. Then we study the corresponding transition semigroup and, more precisely, we prove that it has Feller property and we give an explicit form of an invariant probability of the system.
Version 2: Typos are corrected. Section 6 is reorganised in order to make it more transparent; the results are unchanged. The presentation of the proof of Proposition 3 is improved. Statement of Lemma 5 is rephrased. Version 3: Acknowledgement of financial support is added. Accepted for publication in "Stochastic Partial Differential Equations: Analysis and Computations"