Abstract:Various classes of Gaussian random fields associated with transient Markov processes $Y$ have been introduced in the probability and mathematical physics literature. The present paper is based on a natural class of Gaussian random fields, termed universal Gaussian random fields (UGRF), for an underlying Markov processes $X$, on a state space $(S,\mathcal{S})$ and having an ergodic invariant initial distribution $\pi$, via a central limit theorem of Rabi Bhattacharya for appropriately scaled additive integral functionals $\int_0^{nt}f(X(s))ds = \sum_{j=1}^n\int_{(j-1)t}^{jt}f(X(s))ds$ for $f\in1_\pi^\perp\equiv \{f\in L^2(S,\pi):\langle f,1\rangle_\pi=0\}$. Connections with GRFs associated with Markov processes $Y$ in a sense of Dynkin, and Diaconis and Evans, respectively, are established under additional conditions on the infinitesimal generator $(A,\mathcal{D}(A))$ of the underlying Markov process $X$.
From: Edward Waymire [view email]
[v1]
Fri, 19 Jun 2026 21:19:54 UTC (21 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。