数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (4): 1073-1085.doi: 10.1016/S0252-9602(10)60104-X

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ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS

 Svetlana Jankovic, Dejan Ilic   

  1. University of Ni\v s, Department of Mathematics, Vi\v segradska 33, 18000 Ni\v s, Serbia
  • 收稿日期:2007-08-09 修回日期:2008-08-13 出版日期:2010-07-20 发布日期:2010-07-20
  • 基金资助:

    Supported by Grant No. 144003  of MNTRS

ONE LINEAR ANALYTIC APPROXIMATION FOR STOCHASTIC INTEGRODIFFERENTIAL EQUATIONS

 Svetlana Jankovic, Dejan Ilic   

  1. University of Ni\v s, Department of Mathematics, Vi\v segradska 33, 18000 Ni\v s, Serbia
  • Received:2007-08-09 Revised:2008-08-13 Online:2010-07-20 Published:2010-07-20
  • Supported by:

    Supported by Grant No. 144003  of MNTRS

摘要:

This article concerns the construction of approximate solutions for a general stochastic integrodifferential
equation which is not explicitly solvable and whose coefficients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time
interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the Lp-th norm, uniformly on the time interval. The convergence with probability one is also given.

关键词: Stochastic integrodifferential equation, linear approximation, approximate solution, Lp-convergence,
convergence with probability one

Abstract:

This article concerns the construction of approximate solutions for a general stochastic integrodifferential
equation which is not explicitly solvable and whose coefficients functionally depend on Lebesgue integrals and stochastic integrals with respect to martingales. The approximate equations are linear ordinary stochastic differential equations, the solutions of which are defined on sub-intervals of an arbitrary partition of the time
interval and connected at successive division points. The closeness of the initial and approximate solutions is measured in the Lp-th norm, uniformly on the time interval. The convergence with probability one is also given.

Key words: Stochastic integrodifferential equation, linear approximation, approximate solution, Lp-convergence,
convergence with probability one

中图分类号: 

  • 60H10