Sufficient conditions for the terminal invariance of nonlinear dynamic stochastic controlled systems (jump diffusions) are formulated and proved. The jump component has the form of an integral over a random Poisson measure. The parameters of this measure (the intensity and distribution of the values of jumps) are assumed to change over time. The conditions of invariance with respect to perturbations for a given initial state and also the conditions of absolute invariance (which ensure the constancy of a terminal criterion for any initial state) are proposed. The results are applied to a number of model examples, which include the numerical simulation and analytical study of the designed terminally invariant dynamic systems.

提出并证明了非线性动态随机控制系统（跳跃扩散）的最终不变性的充分条件。跳跃分量具有随机泊松测度上的积分形式。假定此度量的参数（跳跃值的强度和分布）随时间变化。提出了关于给定初始状态的摄动不变性的条件，以及绝对不变性的条件（这确保了对于任何初始状态的最终准则的恒定性）。结果被应用于许多模型实例，包括对设计的最终不变动力系统的数值模拟和分析研究。