带Lévy跳的中立随机微分方程的EM逼近
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摘要
本文研究了一类带Lévy跳的中立随机微分方程的Euler近似解的问题.利用Gronwall不等式、H?lder不等式及BDG不等式,在局部Lipschitz和线性增长条件下,本文给出近似解在均方意义下收敛于真实解,推广了带Poisson跳的中立随机微分方程EM逼近结果.
In this paper, we study the Euler-Maruyama method for Neutral stochastic functional differential equations with Lévy jumps. By using Gronwall inequality,H?lder inequality and BDG inequality, we prove the numerical solution converges to the real solution, which generalize the EM approximation for neutral stochastic functional differential equations with Poisson jumps.
In this paper, we study the Euler-Maruyama method for Neutral stochastic functional differential equations with Lévy jumps. By using Gronwall inequality,H?lder inequality and BDG inequality, we prove the numerical solution converges to the real solution, which generalize the EM approximation for neutral stochastic functional differential equations with Poisson jumps.
引文
[1] Mao X R. Stochastic differential equations and applications[M]. New York:Horwood, 2007.
[2]毛伟.带有Lévy跳和非局部Lipschitz系数的随机泛函微分方程解的存在唯一性[J].数学的实践与认识, 2013, 43(13):193–199.
[3] Mao W, Hu L J, Mao X R. Neutral stochastic functional differential equations with Lévy jumps under the local lipschitz condition[J]. Adv. Diff. Equ., 2017, 57:1–24.
[4] Tan J G, Wang H L, Guo Y F, Zhu Z W. Numerical solutions to neutral stochastic delay differential equations with poisson jumps under local lipschitz condition[J]. Math. Prob. Engin.,http://dx.doi.org/10.1155/2014/976183, 2014.
[5]毛伟. Lévy噪声扰动的混合随机微分方程的Euler近似解[J].华东师范大学学报(自然科学版), 2014,48(1):1–6.
[6]叶俊,李凯.带Markov状态转换的跳扩散方程的数值解[J].数学学报, 2011, 174:1–27.
[7] Yuan C G, Mao X R. Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching[J]. Math. Comput. Simul., 2004, 64:223–235.
[8] Arino O, Burton T, Haddovk J. Periodic solutions to functional differential equations[J]. Proc. R.Soc. Edinb., 1985, 101:253–271.
[9] Kloeden P E, Platen E. Numerical solution of stochastic differential equations[M]. Berlin:Springer,1999.
[2]毛伟.带有Lévy跳和非局部Lipschitz系数的随机泛函微分方程解的存在唯一性[J].数学的实践与认识, 2013, 43(13):193–199.
[3] Mao W, Hu L J, Mao X R. Neutral stochastic functional differential equations with Lévy jumps under the local lipschitz condition[J]. Adv. Diff. Equ., 2017, 57:1–24.
[4] Tan J G, Wang H L, Guo Y F, Zhu Z W. Numerical solutions to neutral stochastic delay differential equations with poisson jumps under local lipschitz condition[J]. Math. Prob. Engin.,http://dx.doi.org/10.1155/2014/976183, 2014.
[5]毛伟. Lévy噪声扰动的混合随机微分方程的Euler近似解[J].华东师范大学学报(自然科学版), 2014,48(1):1–6.
[6]叶俊,李凯.带Markov状态转换的跳扩散方程的数值解[J].数学学报, 2011, 174:1–27.
[7] Yuan C G, Mao X R. Convergence of the Euler-Maruyama method for stochastic differential equations with Markovian switching[J]. Math. Comput. Simul., 2004, 64:223–235.
[8] Arino O, Burton T, Haddovk J. Periodic solutions to functional differential equations[J]. Proc. R.Soc. Edinb., 1985, 101:253–271.
[9] Kloeden P E, Platen E. Numerical solution of stochastic differential equations[M]. Berlin:Springer,1999.