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Stochastic Volterra equations with singular kernels

Author

Listed:
  • Cochran, W. George
  • Lee, Jung-Soon
  • Potthoff, Jürgen

Abstract

Existence, uniqueness and continuity properties of solutions of stochastic Volterra equations with singular integral kernels (driven by Brownian motion) are proven.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:56:y:1995:i:2:p:337-349
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    Citations

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    Cited by:

    1. Aur'elien Alfonsi & Ahmed Kebaier, 2021. "Approximation of Stochastic Volterra Equations with kernels of completely monotone type," Papers 2102.13505, arXiv.org, revised Mar 2022.
    2. Harang, Fabian A. & Tindel, Samy, 2021. "Volterra equations driven by rough signals," Stochastic Processes and their Applications, Elsevier, vol. 142(C), pages 34-78.
    3. Aur'elien Alfonsi & Guillaume Szulda, 2024. "On non-negative solutions of stochastic Volterra equations with jumps and non-Lipschitz coefficients," Papers 2402.19203, arXiv.org, revised Jul 2024.
    4. Alexandre Pannier & Antoine Jacquier, 2019. "On the uniqueness of solutions of stochastic Volterra equations," Papers 1912.05917, arXiv.org, revised Apr 2020.
    5. Herv'e Andr`es & Benjamin Jourdain, 2024. "Existence, uniqueness and positivity of solutions to the Guyon-Lekeufack path-dependent volatility model with general kernels," Papers 2408.02477, arXiv.org.
    6. 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.
    7. Deya, Aurélien & Tindel, Samy, 2011. "Rough Volterra equations 2: Convolutional generalized integrals," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1864-1899, August.
    8. David J. Promel & David Scheffels, 2022. "Pathwise uniqueness for singular stochastic Volterra equations with H\"older coefficients," Papers 2212.08029, arXiv.org, revised Jul 2024.
    9. 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.
    10. Jie, Lijuan & Luo, Liangqing & Zhang, Hua, 2024. "One-dimensional McKean–Vlasov stochastic Volterra equations with Hölder diffusion coefficients," Statistics & Probability Letters, Elsevier, vol. 205(C).
    11. Carsten Chong, 2017. "Lévy-driven Volterra Equations in Space and Time," Journal of Theoretical Probability, Springer, vol. 30(3), pages 1014-1058, September.
    12. Prömel, David J. & Scheffels, David, 2023. "Stochastic Volterra equations with Hölder diffusion coefficients," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 291-315.

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