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Error distribution of the Euler approximation scheme for stochastic Volterra equations

Author

Listed:
  • David Nualart

    (University of Kansas)

  • Bhargobjyoti Saikia

    (University of Kansas)

Abstract

The purpose of this paper is to establish the convergence in distribution of the normalized error in the Euler approximation scheme for stochastic Volterra equations driven by a standard Brownian motion, with a kernel of the form $$(t-s)^\alpha $$ ( t - s ) α , where $$\alpha \in \left( -\frac{1}{2}, \frac{1}{2}\right) $$ α ∈ - 1 2 , 1 2 .

Suggested Citation

  • David Nualart & Bhargobjyoti Saikia, 2023. "Error distribution of the Euler approximation scheme for stochastic Volterra equations," Journal of Theoretical Probability, Springer, vol. 36(3), pages 1829-1876, September.
    • Handle: RePEc:spr:jotpro:v:36:y:2023:i:3:d:10.1007_s10959-022-01222-9
    DOI: 10.1007/s10959-022-01222-9
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    References listed on IDEAS

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    1. Richard, Alexandre & Tan, Xiaolu & Yang, Fan, 2021. "Discrete-time simulation of Stochastic Volterra equations," Stochastic Processes and their Applications, Elsevier, vol. 141(C), pages 109-138.
    2. Wang, Zhidong, 2008. "Existence and uniqueness of solutions to stochastic Volterra equations with singular kernels and non-Lipschitz coefficients," Statistics & Probability Letters, Elsevier, vol. 78(9), pages 1062-1071, July.
    3. Cochran, W. George & Lee, Jung-Soon & Potthoff, Jürgen, 1995. "Stochastic Volterra equations with singular kernels," Stochastic Processes and their Applications, Elsevier, vol. 56(2), pages 337-349, April.
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