标题： 非线性切换扩散系统在有限和无限时间范围内的显式近似方法 显示英文标题

标题： Explicit approximations for nonlinear switching diffusion systems in finite and infinite horizons

摘要： 聚焦于涉及连续动态和离散事件的混合扩散动力学，本文研究了由马尔可夫链调制的非线性切换扩散系统的显式近似。 提出了不同种类易于实现的显式格式，以逼近具有局部Lipschitz连续漂移和扩散系数的切换扩散系统在有限和无限区间内的动态行为。 在除了保证精确解具有其动态性质的条件外，无需其他限制条件，数值解在有限时间范围内强收敛于精确解，并且实现了对长时间动态性质包括矩有界性、稳定性和遍历性的近似。 提供了一些模拟和例子来支持理论结果并证明该方法的有效性。 显示英文摘要

摘要： Focusing on hybrid diffusion dynamics involving continuous dynamics as well as discrete events, this article investigates the explicit approximations for nonlinear switching diffusion systems modulated by a Markov chain. Different kinds of easily implementable explicit schemes have been proposed to approximate the dynamical behaviors of switching diffusion systems with local Lipschitz continuous drift and diffusion coefficients in both finite and infinite intervals. Without additional restriction conditions except those which guarantee the exact solutions posses their dynamical properties, the numerical solutions converge strongly to the exact solutions in finite horizon, moreover, realize the approximation of long-time dynamical properties including the moment boundedness, stability and ergodicity. Some simulations and examples are provided to support the theoretical results and demonstrate the validity of the approach.