Girsanov theorem for stochastic flows with interaction

• Date: 2009
• Main Authors: Malovichko, T. V., Маловичко, Т. В.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2009
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3025
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove an analog of the Girsanov theorem for the stochastic differential equations with interaction $$dz(u,t) = a(z(u,t),μt)dt + ∫R f(z(u,t)−p)W(dp,dt),$$ where $W$ is a Wiener sheet on $ℝ × [0; +∞)$ and $a(∙)$ is a function of special type.