Open Access
2018 Split-step collocation methods for stochastic Volterra integral equations
Y. Xiao, J.N. Shi, Z.W. Yang
J. Integral Equations Applications 30(1): 197-218 (2018). DOI: 10.1216/JIE-2018-30-1-197


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.


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Y. Xiao. J.N. Shi. Z.W. Yang. "Split-step collocation methods for stochastic Volterra integral equations." J. Integral Equations Applications 30 (1) 197 - 218, 2018.


Published: 2018
First available in Project Euclid: 10 April 2018

zbMATH: 06873405
MathSciNet: MR3784889
Digital Object Identifier: 10.1216/JIE-2018-30-1-197

Primary: 34K05 , 35B33

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

Rights: Copyright © 2018 Rocky Mountain Mathematics Consortium

Vol.30 • No. 1 • 2018
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