Journal of Integral Equations and Applications

Split-step collocation methods for stochastic Volterra integral equations

Y. Xiao, J.N. Shi, and Z.W. Yang

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Abstract

In this paper, a split-step collocation method is proposed for solving linear stochastic Volterra integral equations (SVIEs) with smooth kernels. The H\"older condition and the conditional expectations of the exact solutions are investigated. The solvability and mean-square boundedness of numerical solutions are proved and the strong convergence orders of collocation solutions and iterated collocation solutions are also shown. In addition, numerical experiments are provided to verify the conclusions.

Article information

Source
J. Integral Equations Applications, Volume 30, Number 1 (2018), 197-218.

Dates
First available in Project Euclid: 10 April 2018

Permanent link to this document
https://projecteuclid.org/euclid.jiea/1523347345

Digital Object Identifier
doi:10.1216/JIE-2018-30-1-197

Mathematical Reviews number (MathSciNet)
MR3784889

Zentralblatt MATH identifier
06873405

Subjects
Primary: 34K05: General theory 35B33: Critical exponents

Keywords
Stochastic Volterra integral equations split-step collocation methods split-step backward Euler method strong convergence order

Citation

Xiao, Y.; Shi, J.N.; Yang, Z.W. Split-step collocation methods for stochastic Volterra integral equations. J. Integral Equations Applications 30 (2018), no. 1, 197--218. doi:10.1216/JIE-2018-30-1-197. https://projecteuclid.org/euclid.jiea/1523347345


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