某些马格努斯型方案在加性分数布朗运动和泊松随机量驱动的非自治抛物 SPDE 的有限元离散化中的强收敛性

Aurelien Junior Noupelah, Jean Daniel Mukam, Antoine Tambue
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引用次数: 0

摘要

这项工作的目的是提供一般二阶非自治半线性随机偏微分方程(SPDE)的数值近似的强收敛性结果,该近似同时由Hurst参数H (1/2,1)和泊松随机度量的加分布朗运动(fBm)驱动,在模拟现实世界的现象时更为现实。空间逼近采用标准有限元法,时间逼近采用随机马格努斯型积分法或线性隐式欧拉法。我们研究了完全离散方案的均方误差估计,结果表明收敛阶数如何依赖于初始数据和驱动过程的规则性。据我们所知,这两种方案是第一种近似非自治半线性随机偏微分方程(SPDE)的数值方法,该方程同时由具有 Hurst 参数 H 的加性分数布朗运动和泊松随机度量驱动。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Strong convergence of some Magnus-type schemes for the finite element discretization of non-autonomous parabolic SPDEs driven by additive fractional Brownian motion and Poisson random measure
The aim of this work is to provide the strong convergence results of numerical approximations of a general second order non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive fractional Brownian motion (fBm) with Hurst parameter H \in (1/2,1) and a Poisson random measure, more realistic in modelling real world phenomena. Approximations in space are performed by the standard finite element method and in time by the stochastic Magnus-type integrator or the linear semi-implicit Euler method. We investigate the mean-square errors estimates of our fully discrete schemes and the results show how the convergence orders depend on the regularity of the initial data and the driven processes. To the best of our knowledge, these two schemes are the first numerical methods to approximate the non-autonomous semilinear stochastic partial differential equation (SPDE) driven simultaneously by an additive fractional Brownian motion with Hurst parameter H and a Poisson random measure.
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