Self attracting diffusions: a periodic case
Carl-Erik Gauthier · arXiv (Cornell University) · 2015
This paper proves almost-sure convergence for a new type of self-attracting diffusion given by the stochastic differential equation: $$dX_{t}=\sigma dW_{t}+a\int_{0}^{t}\sin(X_{t}-X_{s})dsdt, $$ where $\sigma >0$, $(W_{t})_{t\geqslant 0}$ is a real Brownian motion and $a < 0$.