论文标题
马尔可夫过程的随机潜力
Random potentials for Markov processes
论文作者
论文摘要
该论文专用于积分函数$ \ int_0^\ infty f（x_t）\，{\ mathrm {d} t} $在$ \ x $的情况下，在$ \ x $的情况下，在$ \ x $中。可以确定，可以将这些功能作为积分$ \ int _ {\ x} f（y）\ g（x，x，\ mathrm {d} y，ω）$具有矢量值随机度量$ \ g（x，x，\ mathrm {d} y，ω）$。考虑了一些示例，例如复合泊松过程，布朗运动和扩散。
The paper is devoted to the integral functionals $\int_0^\infty f(X_t)\,{\mathrm{d}t}$ of Markov processes in $\X$ in the case $d\ge 3$. It is established that such functionals can be presented as the integrals $\int_{\X} f(y) \G(x, \mathrm{d}y, ω)$ with vector valued random measure $\G(x, \mathrm{d}y, ω)$. Some examples such as compound Poisson processes, Brownian motion and diffusions are considered.
