论文标题
混合随机微分方程和首次通过特性的空间网格近似
Space-grid approximations of hybrid stochastic differential equations and first passage properties
论文作者
论文摘要
混合随机微分方程是一种有用的工具，可以建模连续变化的随机系统，该系统由可能取决于系统状态本身的随机环境调节。在本文中，我们通过空间网格离散化建立了溶液向混合随机微分方程的路径收敛。虽然有时间网格离散是用于模拟目的的经典方法，但我们的空间网格离散化提供了与多项式马尔可夫调制的布朗尼动作的联系，从而导致了计算障碍。我们利用我们的收敛结果来获得对解决方案混合随机微分方程的第一次通过概率和预期职业时间的有效近似值，这是这种强大框架的第一个结果。我们最终说明了在数值示例中所产生的近似值的性能。
Hybrid stochastic differential equations are a useful tool to model continuously varying stochastic systems which are modulated by a random environment that may depend on the system state itself. In this paper, we establish the pathwise convergence of the solutions to hybrid stochastic differential equations via space-grid discretizations. While time-grid discretizations are a classical approach for simulation purposes, our space-grid discretization provides a link with multi-regime Markov modulated Brownian motions, leading to computational tractability. We exploit our convergence result to obtain efficient approximations to first passage probabilities and expected occupation times of the solutions hybrid stochastic differential equations, results which are the first of their kind for such a robust framework. We finally illustrate the performance of the resulting approximations in numerical examples.
