4 problems

Polarity–local times equivalence. Points are polar for $X$ if and only if

A Gaussian stochastic field is a stochastic field whose finite-dimensional distributions are Gaussian. Its boundary behaviour means the behaviour of the field when restricted to th…

Let $\xi$, $T_{\xi}$, and $|T_{\xi}|$ be as in the conditioned Galton–Watson tree theorem, and write $\sigma^2=\operatorname{Var}\xi$. Let $H_n^{\xi}$ and $C_n^{\xi}$ denote respec…

Let $B=(B_t)_{t\geq 0}$ be Brownian motion, let $L_t^x$ denote its local time at $x\in\mathbb{R}$, and define the increment … Let $Z\sim\mathcal{N}(0,1)$ be independent of…