Self-Interacting Diffusions : Symmetric Interactions
| dc.creator | Benaim, Michel | |
| dc.creator | Raimond, Olivier | |
| dc.date | 2003-09-22 | |
| dc.date.accessioned | 2026-07-07T05:01:21Z | |
| dc.date.available | 2026-07-07T05:01:21Z | |
| dc.description | Let $M$ be a compact Riemannian manifold. A {\em self-interacting diffusion} on $M$ is a stochastic process solution to $$dX_t = dW_t(X_t) - \frac{1}{t}(\int_0^t \nabla V_{X_s}(X_t)ds)dt$$ where $\{W_t\}$ is a Brownian vector field on $M$ and $V_x(y) = V(x,y)$ a smooth function. Let $μ_t = \frac{1}{t} \int_0^t δ_{X_s} ds$ denote the normalized occupation measure of $X_t$. We prove that, when $V$ is symmetric, $μ_t$ converges almost surely to the critical set of a certain nonlinear free energy functional $J$. Furthermore, $J$ has generically finitely many critical points and $μ_t$ converges almost surely toward a local minimum of $J.$ Each local minimum having a positive probability to be selected. | |
| dc.identifier | https://arxiv.org/abs/math/0309356 | |
| dc.identifier | http://arxiv.org/abs/math/0309356 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/68637 | |
| dc.subject | Probability | |
| dc.title | Self-Interacting Diffusions : Symmetric Interactions | |
| dc.type | text |