All Questions

For closed manifolds, we know that the Poisson boundary is trivial due to compactness and for radially symmetric manifolds for which diffusion is one dimensional, there are A Brief Introduction to ...

As we know, the random walk on $\mathbb{Z}/n$ will converge(in some sense) to the Brownian motion on $\mathbb{R}$ when $n\to\infty$. I would like to know is there some higher dimensional analogy ...

I would like to have an Itô Diffusion $$ X_t = \int_0^t b(s) \mathrm{d}s + \int_0^t \sigma(s) \mathrm{d}B_s.$$ where the (vector- and matrix-valued, respectively) functions $b$ and $\sigma$ have lower ...