随机边值问题的唯一律
Uniqueness in Law for Stochastic Boundary Value Problems
摘要：
研究了二阶常随机微分方程在给定区间上Dirichlet边值问题解的存在唯一性。在本文的第一部分中，我们提供了保证路径唯一性的充分条件，推广了一些已知的结果。第二部分给出了弱唯一性概念的充分条件，并给出了一个有意义的例子。这样的条件涉及一个线性化方程，是不同的类型，相对于那些通常施加研究路径的唯一性。这似乎是第一个文件，其中涉及法律的唯一性（预期）随机边值问题。我们主要使用泛函分析工具和Malliavin微积分的一些概念。
英文摘要：
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure pathwise uniqueness, extending some known results. In the second part we show sufficient conditions to have the weaker concept of uniqueness in law and provide a significant example. Such conditions involve a linearized equation and are of different type with respect to the ones which are usually imposed to study pathwise uniqueness. This seems to be the first paper which deals with uniqueness in law for (anticipating) stochastic boundary value problems. We mainly use functional analytic tools and some concepts of Malliavin Calculus.
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