Volume 26, Issue 3
Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability

Guoli Zhou, Boling GuoZhenting Hou

J. Part. Diff. Eq., 26 (2013), pp. 251-288.

Published online: 2013-09

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  • Abstract

The existence and uniqueness of mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by Levy process. Then the authors prove the moment exponential stability, almost sure exponential stability and comparison principles of the mild solution. As applications, the stability and comparison principles of stochastic heat equation with Levy jump are given.

  • Keywords

Stochastic evolution equation Levy processes mild solution stability

  • AMS Subject Headings

74H55, 60H15

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

zhouguoli736@126.com (Guoli Zhou)

gbl@iapcm.ac.cn (Boling Guo)

zthou@csu.edu.cn (Zhenting Hou)

  • BibTex
  • RIS
  • TXT
@Article{JPDE-26-251, author = {Zhou , Guoli and Guo , Boling and Hou , Zhenting}, title = {Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability}, journal = {Journal of Partial Differential Equations}, year = {2013}, volume = {26}, number = {3}, pages = {251--288}, abstract = {

The existence and uniqueness of mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by Levy process. Then the authors prove the moment exponential stability, almost sure exponential stability and comparison principles of the mild solution. As applications, the stability and comparison principles of stochastic heat equation with Levy jump are given.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v26.n3.4}, url = {http://global-sci.org/intro/article_detail/jpde/5164.html} }
TY - JOUR T1 - Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability AU - Zhou , Guoli AU - Guo , Boling AU - Hou , Zhenting JO - Journal of Partial Differential Equations VL - 3 SP - 251 EP - 288 PY - 2013 DA - 2013/09 SN - 26 DO - http://doi.org/10.4208/jpde.v26.n3.4 UR - https://global-sci.org/intro/article_detail/jpde/5164.html KW - Stochastic evolution equation KW - Levy processes KW - mild solution KW - stability AB -

The existence and uniqueness of mild solution to stochastic equations with jumps are established, a stochastic Fubini theorem and a type of Burkholder-Davis-Gundy inequality are proved, and the two formulas are used to study the regularity property of the mild solution of a general stochastic evolution equation perturbed by Levy process. Then the authors prove the moment exponential stability, almost sure exponential stability and comparison principles of the mild solution. As applications, the stability and comparison principles of stochastic heat equation with Levy jump are given.

Guoli Zhou, Boling Guo & Zhenting Hou. (2019). Mild Solution of Stochastic Equations with Lèvy Jumps: Existence, Uniqueness, Regularity and Stability. Journal of Partial Differential Equations. 26 (3). 251-288. doi:10.4208/jpde.v26.n3.4
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