We study the game problem of approach for a system whose dynamics is described by a stochastic differential equation in a Hilbert space. The main assumption on the equation is that the operator multiplying the system state generates a strongly continuous semigroup (a semigroup of class \(C_{0}\)). Solutions of the equation are represented by a stochastic variation of constants formula. Using constraints on the support functionals of sets defined by the behavior of the pursuer and the evader, we obtain conditions for the approach of the system state to a cylindrical terminal set. The results are illustrated with a model example of a simple motion in a Hilbert space with random perturbations. Applications to distributed systems described by stochastic partial differential equations are considered. By taking into account a random external influence, we consider the heat propagation process with controlled distributed heat sources and sinks.

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关于随机系统中的微分博弈

我们研究一个系统的动力学问题，该系统的动力学由希尔伯特空间中的随机微分方程描述。该方程式的主要假设是，运算符乘以系统状态会生成一个强连续半群（类\（C_ {0} \）的半群 ）。方程的解由常数公式的随机变化表示。使用由追随者和逃避者的行为定义的集合的支持功能的约束，我们获得了将系统状态逼近圆柱形终端的条件。通过希尔伯特空间中具有随机扰动的简单运动的模型示例来说明结果。考虑了用随机偏微分方程描述的分布式系统的应用。通过考虑随机的外部影响，我们考虑了受控分布热源和散热片的传热过程。