凸区域中具有反射的随机弦
A random string with reflection in a convex domain
摘要：
研究了随机弦在$\R^d$中的凸区域$O$中的运动，即向量值随机热方程的解，该解被限制在$O$的闭包中，并反映在$O$的边界上.我们研究了反射测度的结构，通过计算其Revuz测度的无限维分部积分法公式。我们的方法利用最近的结果弱收敛的马尔可夫过程与对数凹不变测度。
英文摘要：
We study the motion of a random string in a convex domain $O$ in $\R^d$, namely the solution of a vector-valued stochastic heat equation, confined in the closure of $O$ and reflected at the boundary of $O$. We study the structure of the reflection measure by computing its Revuz measure in terms of an infinite-dimensional integration by parts formula. Our method exploits recent results on weak convergence of Markov processes with log-concave invariant measures.
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