Abstract
Random motions on Spheres
Abstract: The talk is based on joint work with Zdzisław Brzeźniak. First, we introduce several classes of SDEs on $mathbb{R}^{d+1}$ preserving the sphere $mathbb{S}^d$, whose restrictions to $mathbb{S}^d$ are Markov processes generated by the Laplace-Beltrami operator $Delta_{mathbb{S}^d}$.
Then, we are interested in the jump diffusions preserving $mathbb{S}^d$. We argue that they should be considered in the Marcus canonical form. Special emphasis will be placed on rotationally invariant diffusions. In this case, we will calculate the generator kernels.