分数 L\'{e}vy过程的随机积分及其驱动的随机微分方程

Abstract

Abstract:

In this paper, based on the white noise analysis of square integrable pure-jump L\'{e}vy process given by [1], we define the formal derivative of fractional L\'{e}vy process defined by the square integrable pure-jump L\'{e}vy process as the fractional L\'{e}vy noises by considering fractional L\'{e}vy process as the generalized functional of L\'{e}vy process, and then we define the Skorohod integral with respect to the fractional L\'{e}vy process. Moreover, we propose a class of stochastic Volterra equations driven by fractional L\'{e}vy noises and investigate the existence and uniqueness of their solutions; In addition, we propose a class of stochastic differential equations driven by fractional L\'{e}vy noises and prove that under the Lipschtz and linear conditions there exists unique stochastic distribution-valued solution.

Key words: White noise analysis, Fractional L\{e}vy processes, Skorohod integral, Stochastic differential equations

CLC Number:

60E07

LV Xue-Bin, DAI Wan-Yang. Stochastic Integration for Fractional L\'{e}vy Processes and Stochastic Differential Equations Driven by Fractional L\'{e}vy Noises[J].Acta mathematica scientia,Series A, 2013, 33(6): 1022-1034.

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References

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Stochastic Integration for Fractional L\'{e}vy Processes and Stochastic Differential Equations Driven by Fractional L\'{e}vy Noises

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