论文标题
在流动上的设定值二重过程的构建
Construction of set-valued dual processes on manifolds
论文作者
论文摘要
本文的目的是构建一个布朗运动$ x：=（x_t）_ {t \ geq 0} $在Riemannian歧管$ m $中取值，以及紧凑的值$ d：=（d_t）_ {t \ geq 0} $ $ {\ mathscr f}_τ^d $，$x_τ$的定律是$d_τ$上的归一化lebesgue度量。这种相互交织的结果是对Pitman定理的概括。我们首先构建与Stokes定理有关的常规互相交织过程。然后，使用几个限制过程，我们构建同步交织，自由交织的，镜像相互交织的过程。布朗运动在（形态）骨骼或$ d $的边界上的当地时代起着重要作用。研究了几个具有移动间隔，圆盘，环，对称凸组的示例。 关键词：关于黎曼流形的布朗动作，相互交织的关系，设定值的双重过程，原始过程和双重过程的耦合，随机平均曲率演变，当地边界和骨骼时代，普遍的皮特曼定理。
The purpose of this paper is to construct a Brownian motion $X := (X_t)_{t\geq 0}$ taking values in a Riemannian manifold $M$, together with a compact valued process $D:= (D_t)_{t\geq 0}$ such that, at least for small enough ${\mathscr F}^D$-stopping time $τ> 0$ and conditioned by ${\mathscr F}_τ^D$, the law of $X_τ$ is the normalized Lebesgue measure on $D_τ$. This intertwining result is a generalization of Pitman theorem. We first construct regular intertwined processes related to Stokes' theorem. Then using several limiting procedures we construct synchronous intertwined, free intertwined, mirror intertwined processes. The local times of the Brownian motion on the (morphological) skeleton or the boundary of $D$ plays an important role. Several examples with moving intervals, discs, annulus, symmetric convex sets are investigated. KEYWORDS: Brownian motions on Riemannian manifolds, intertwining relations, set-valued dual processes, couplings of primal and dual processes, stochastic mean curvature evolutions, boundary and skeleton local times, generalized Pitman theorem.
