Brownian Motion in a Hilbert Space with a Semipermeable Membrane on a Hyperplane

• Date: 2001
• Main Authors: Zaitseva, L. L., Зайцева, Л. Л.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2001
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4310
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In a separable Hilbert space, we construct a continuous Markov process whose behavior coincides everywhere, except for a hyperplane S orthogonal to a given unit vector ν, with the behavior of a homogeneous Gaussian process with a given correlation operator tB, where B is a nonsingular nuclear operat...