Stochastic PDEs in S′ for SDEs driven by Levy noise

被引：1

作者：

Bhar, Suprio ^{[1
]}

Bhaskaran, Rajeev ^{[2
]}

Sarkar, Barun ^{[3
]}

机构：

[1] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur 208016, Uttar Pradesh, India

[2] Indian Stat Inst Bangalore Ctr, Theoret Stat & Math Unit, 8th Mite Mysore Rd, Bangalore 560059, Karnataka, India

[3] TIFR Ctr Applicable Math, Bangalore 560065, Karnataka, India

来源：

RANDOM OPERATORS AND STOCHASTIC EQUATIONS | 2020年 / 28卷 / 03期

关键词：

S '-valued process; Levy processes; Hermite Sobolev space; strong solution; monotonicity inequality; translation invariance; PROBABILISTIC REPRESENTATIONS; FORMULA; SPACE;

D O I：

10.1515/rose-2020-2041

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this article we show that a finite-dimensional stochastic differential equation driven by a Levy noise can be formulated as a stochastic partial differential equation (SPDE) driven by the same Levy noise. We prove the existence result for such an SPDE by Ito'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.

引用

页码：217 / 226

页数：10

共 32 条

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