On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations
On the Rate of Convergence for Monotone Numerical Schemes for Nonlocal Isaacs Equations
复制标题
非局部艾萨克斯方程单调数值格式的收敛率
DOI：
10.1137/17m114995x
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
E. Jakobsen
中科院分区：
文献类型：
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作者：
Imran H. Biswas;I. Chowdhury;E. Jakobsen
研究了非局部Isaacs方程的单调数值格式，这类方程是具有跳扩散状态过程的随机微分对策的动态规划方程。这些方程是阶数小于2 $的完全非线性非凸方程。在本文中，他们也被允许是退化的，并有非光滑的解决方案。的主要贡献是一系列新的先验误差估计：第一个结果为非本地艾萨克斯方程，第一个一般结果退化的非凸方程的顺序大于1 $，第一个结果在粘度的解决方案的设置给予精确的依赖分数阶的方程。我们还观察到一个新的现象，即当非局部扩散系数依赖于$x$和$t$，仅依赖于$x$，或两者都不依赖时，速率不同。
We study monotone numerical schemes for nonlocal Isaacs equations, the dynamic programming equations of stochastic differential games with jump-diffusion state processes. These equations are fully-nonlinear non-convex equations of order less than $2$. In this paper they are also allowed to be degenerate and have non-smooth solutions. The main contribution is a series of new a priori error estimates: The first results for nonlocal Isaacs equations, the first general results for degenerate non-convex equations of order greater than $1$, and the first results in the viscosity solution setting giving the precise dependence on the fractional order of the equation. We also observe a new phenomena, that the rates differ when the nonlocal diffusion coefficient depend on $x$ and $t$, only on $x$, or on neither.