Self-repelling diffusions via an infinite dimensional approach

TL;DR

This paper investigates self-interacting diffusions using an infinite dimensional framework, establishing existence, uniqueness, and properties of the associated transition semigroup, including an explicit invariant measure.

Contribution

It introduces an infinite dimensional approach to analyze self-repelling diffusions, proving key properties and explicitly characterizing the invariant measure.

Findings

Existence and uniqueness of solutions with Markov property

Transition semigroup has Feller property

Explicit form of the invariant probability measure

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.