一类带跳的随机微分方程解的Harnack不等式
PDF下载 (435)王彦涛,朱全新*.一类带跳的随机微分方程解的Harnack不等式[J].宁波大学学报(理工版),2015,28(01):70-75.DOI:
WANG Yan-tao,ZHU Quan-xin*.Harnack Inequality for the Solution of a Class of Stochastic Differential Equations with Jumps[J].Journal of Ningbo University(Natural Science & Engineering Edition),2015,28(01):70-75.DOI:
| Title: | Harnack Inequality for the Solution of a Class of Stochastic Differential Equations with Jumps |
| 作者: | 王彦涛, 朱全新* |
| Author(s): | WANG Yan-tao, ZHU Quan-xin* |
| 关键词: | 耦合; Harnack不等式; 测度变换; 泊松点过程 |
| Keywords: | coupling; Harnack inequality; the change of measure; poisson point process |
| 分类号: | O211.63 |
| 文献标识码: | A |
| 摘要: | 针对一类带泊松跳的随机微分方程, 在一些合理的条件假设下研究了该类方程解的半群的Harnack不等式和Log-Harnack不等式问题. 首先建立了两类半群之间的关系, 同时使用耦合方法, 结合Girsanov定理、H?lder不等式、Young不等式以及Ito公式, 先后获得了Harnack和Log-Harnack的2种不等式 |
| Abstract: | In this paper, we study a class of stochastic differential equations with Poission jumps. Under some reasonable conditions, we deal with the issue of the Harnack inequalities and the Log-Harnack inequalities for the semigroup of the solutions of such equations. We establish the relationship between the two kinds of semigroup. We also obtain two inequalities such as Harnack and Log-Harnack using the coupling argument, along with Girsanov theorem, H?lder inequality, Young inequality and Ito formula |
| 参考文献 /References: | [1].ématiques, 2006, 130(3):223-233. [2].Wang Fengyu, Yuan Ciguang. Harnack inequality and applications for stochastic differential equations with jumps[J]. 2008, Available at arXiv:0801.2668. [3].Wang Fengyu Yuan Ciguang. Harnack inequalities for functional SDEs with multiplicative noise and applica- tions[J]. Appl Stochastic Process, 2011, 121(11):2692- 2710. [4].Wang Fengyu. Harnack inequality for SDE with multiplicative noise and extension to Neumann semi- group on noncompact Riemannian manifolds[J]. The Annals of probability, 2011, 39(4):1449-1467. [5].Wang Fengyu. Coupling for Ornstein-Uhlenbeck process with jumps[J]. Brenoulli, 2011, 17(4):1136-1158. [6].Wang Fengyu, Wang Jian. coupling and strong feller for jump process on banach space[J]. Probability Theorey and Related Fleds, 2013, 123(5):1588- 1615. [7].Krystul J. Modeling of stochastic hybird systems with applications to accident risk assessment[M]. Netherland: W?hrmann Printing Service, 2006:56-68. [8].龚光鲁. 随机微分方程引论[M]. 2版. 北京: 北京大学出版社, 1995:486. [9].Rong Situ. Theorey of stochastic differential with jumps and applications[M]. 北京: 世界图书出版公司北京公司, 2012:96. [10].Wang Fengyu. Harnack inequalities on manifolds with boundary and applications[J]. J Math Pures Appl, 2010, 94(3):304-321. |
| 备注/Memo: | 收稿日期: 2013?10?19. 宁波大学学报（理工版）网址: http://journallg.nbu.edu.cn/ 基金项目: 国家自然科学基金（60874088, 11101441）; 浙江省自然科学基金（LY12F03010, LQ13A010020）; 宁波大学王宽诚基金; 高等学校 博士学科点新教师基金（20100171120041）. 第一作者: 王彦涛（1985－）, 男, 陕西商洛人, 在读硕士研究生, 主要研究方向: 随机微分方程. E-mail: wangyantao19850131@126.com *通信作者: 朱全新（1975－）, 男, 湖南郴州人, 博导/教授, 主要研究方向: 马氏过程与随机微分方程. E-mail: zhuquanxin@nbu.edu.cn 宁波大学学报（理工版）网址：http://journallg.nbu.edu.cn/ |
