Jump-diffusions in Hilbert spaces: existence, stability and numerics

Jump-diffusions in Hilbert spaces: existence, stability and numerics
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希尔伯特空间中的跳跃扩散：存在性、稳定性和数值

DOI：
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发表时间：
2008
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影响因子：
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通讯作者：
J. Teichmann
J. Teichmann
中科院分区：
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文献类型：
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作者：
D. Filipović;Stefan Tappe;J. Teichmann

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利用移动标架方法，建立了由无限维Wiener过程和补偿Poisson随机测度驱动的具有路径依赖系数的随机偏微分方程（SPDE）的弱解和弱解的存在性、唯一性和稳定性结果.我们的方法是基于一个时间相关的坐标变换，减少了广泛的一类SPDE一类更简单的随机微分方程（随机微分方程）的问题。我们试图提出最普遍的结果，我们可以在我们的设置，在一个独立的框架内，以证明我们的方法在所有细节。此外，几个数值方法SPDE在这种设置的精神。
By means of an original approach, called ‘method of the moving frame’, we establish existence, uniqueness and stability results for mild and weak solutions of stochastic partial differential equations (SPDEs) with path-dependent coefficients driven by an infinite-dimensional Wiener process and a compensated Poisson random measure. Our approach is based on a time-dependent coordinate transform, which reduces a wide class of SPDEs to a class of simpler SDE (stochastic differential equation) problems. We try to present the most general results, which we can obtain in our setting, within a self-contained framework to demonstrate our approach in all details. Also, several numerical approaches to SPDEs in the spirit of this setting are presented.