Self attracting diffusions on a sphere and application to a periodic case
Carl-Erik Gauthier · Electronic Communications in Probability · 2016
This paper proves almost-sure convergence for the self attracting diffusion on the unit sphere \[ dX_t= u \circ dW_{t}(X_t)-a\int _{0}^{t} abla _{\mathbb{S} ^n}V_{X_s}(X_t) dsdt,\qquad X_0=x\in \mathbb{S} ^n, \] where $ u >0$, $a 0$.