Markov调制的随机微分方程极小解与极大解的存在性
Existence of minimal and maximal solutions of stochastic differential equations with Markovian switching
摘要
运用比较方法,在较为一般的条件下,证明了一维M arkov调制的随机微分方程极小解与极大解的存在性。
This paper is concerned with the existence of minimal and maximal solutions of 1 - dimensional stochastic differential equation with Markovian switching under rather mild conditions for coefficients. To this usual comparison methods is used.
出处
《湖北师范学院学报(自然科学版)》
2007年第2期39-42,共4页
Journal of Hubei Normal University(Natural Science)
基金
湖北省教育厅重点项目(2005D2202)
关键词
MARKOV过程
随机微分方程
极小解
极大解
Markov process
stochastic differential equation
minimal solution
maximal solution.
参考文献6
-
1Mao X F. Stability of stochastic differential equations with Markovian switching [ J ]. Stochastic Processes and their Appl, 1999,79(4) :45 -60.
-
2Laksimikantham V,Zhang B G. On the method of sample upper and lower solutions for stochastic differential equations, Stochastic Anal[J]. And Appl,1985,3(3) :341 -347.
-
3Ki Sik Ha ,Jai Heui Kim, Monotone iterative technique for 1 -dimensional stochastic differential equations, Stochastic Anal[J]. And Appl,1988,6(2):191 -203.
-
4Ikeda N and watanabe S. Stochastic differential equations and diffusion processes [ M ]. New York: North - Holland Publishing Company, 1981.
-
5徐立峰.Markov调制的随机微分方程解的比较定理[J].湖北师范学院学报(自然科学版),2006,26(2):31-34. 被引量:1
-
6龚光鲁.随机微分方程引论(第二版)[M].北京:北京大学出版社,1976.
二级参考文献5
-
1Ji Y,Chizeck H J.Controllability,stability and continuous-time Markovian jump linear quadratic control[J].IEEE Trans Automat Control,1990,35:777~789.
-
2龚光鲁.随机微分方程引论(第二版)[M].北京:北京大学出版社,1976.
-
3Ikeda N,watanabe S.Stochastic differential equations and diffusion processes[M].New York:Morlh-Holland Publishing Company.
-
4Yamato T,Wataaabe S.On the uniqueness of solutions of stochastic differential equations[J].Math Kyato Univ 1971,(11):155~167.
-
5Mao X F.Stability of stochastic differential equations with Markovian switching[J].Stochastic Processes and their Appl,1999,79:45~67.
-
1高树玲,赵苗婵.含有一个参数的一阶微分方程极值解的存在性[J].河南教育学院学报(自然科学版),2008,17(3):12-14.
-
2高树玲,赵苗婵.含有一个参数的一阶微分方程极值解的存在性[J].周口师范学院学报,2008,25(5):21-23.
-
3张小芝,叶梅燕,罗清雨.一阶脉冲时滞微分方程的周期边值问题[J].曲阜师范大学学报(自然科学版),2007,33(4):23-28.