Radial processes on $\mathrm{RCD}^*(K,N)$ spaces

We establish a stochastic expression of radial processes $d(p,X_t)=r_p(X_t)$ on RCD${}^*(K,N)$-space for $K\in R$ and $N\in[1,\infty[$ under the law for quasi-everywhere starting point. Moreover, under a condition for the reference point $p$, we can strengthen the expression under the law for everywhere starting point. As a corollary, we obtain various kind comparison theorems on radial process, heat kernel and so on.  This is a joint work with Kazumasa Kuwada.