Uniqueness in Law for Stochastic Boundary Value Problems

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• 作者：Anna Capietto (1) anna.capietto@unito.it
  Enrico Priola (1) enrico.priola@unito.it
• 关键词：Stochastic boundary value problems – ; Anticipative Girsanov theorem – ; Uniqueness in law
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2011
• 出版时间：September 2011
• 年：2011
• 卷：23
• 期：3
• 页码：613-648
• 全文大小：422.0 KB
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• 作者单位：1. Dipartimento di Matematica, Universit脿 di Torino, Via Carlo Alberto 10, 10123 Torino, Italy
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Ordinary Differential Equations
  Partial Differential Equations
  Applications of Mathematics
  
• 出版者：Springer Netherlands
• ISSN：1572-9222

文摘

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.