在𝒮'中随机偏微分方程的lsamvy噪声驱动

IF 0.3 Q4 STATISTICS & PROBABILITY

Random Operators and Stochastic Equations Pub Date : 2020-08-29 DOI:10.1515/rose-2020-2041

Suprio Bhar, R. Bhaskaran, Barun Sarkar

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引用次数: 0

摘要

在本文中，我们证明了一个有限维随机微分方程可以被表示为一个随机偏微分方程(SPDE)。我们利用Itô平移算子的公式证明了这种SPDE的存在性，并利用先前在扩散情况下证明的“单调性不等式”的一种改编形式证明了它的唯一性。因此，我们构造的解具有“平移不变性”的性质。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Stochastic PDEs in 𝒮' for SDEs driven by Lévy noise

Abstract In this article we show that a finite-dimensional stochastic differential equation driven by a Lévy noise can be formulated as a stochastic partial differential equation (SPDE) driven by the same Lévy noise. We prove the existence result for such an SPDE by Itô’s formula for translation operators, and the uniqueness by an adapted form of “Monotonicity inequality”, proved earlier in the diffusion case. As a consequence, the solutions that we construct have the “translation invariance” property.

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来源期刊

Random Operators and Stochastic Equations STATISTICS & PROBABILITY-

CiteScore

0.60

自引率

25.00%

发文量