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Operators associated with a stochastic differential equation driven by fractional Brownian motions

Author

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  • Baudoin, Fabrice
  • Coutin, Laure

Abstract

In this paper, by using a Taylor type development, we show how it is possible to associate differential operators with stochastic differential equations driven by fractional Brownian motions. As an application, we deduce that invariant measures for such SDE's must satisfy an infinite dimensional system of partial differential equations.

Suggested Citation

  • Baudoin, Fabrice & Coutin, Laure, 2007. "Operators associated with a stochastic differential equation driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 117(5), pages 550-574, May.
    • Handle: RePEc:eee:spapps:v:117:y:2007:i:5:p:550-574
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    Citations

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    Cited by:

    1. Yaozhong Hu & Samy Tindel, 2013. "Smooth Density for Some Nilpotent Rough Differential Equations," Journal of Theoretical Probability, Springer, vol. 26(3), pages 722-749, September.
    2. Yuzuru Inahama, 2010. "A Stochastic Taylor-Like Expansion in the Rough Path Theory," Journal of Theoretical Probability, Springer, vol. 23(3), pages 671-714, September.
    3. Baudoin, Fabrice & Ouyang, Cheng, 2011. "Small-time kernel expansion for solutions of stochastic differential equations driven by fractional Brownian motions," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 759-792, April.
    4. Hufei Li & Shaojuan Ma, 2023. "The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise," Mathematics, MDPI, vol. 11(13), pages 1-16, June.
    5. Sreekar Vadlamani, 2010. "Fractional Brownian Flows," Journal of Theoretical Probability, Springer, vol. 23(1), pages 257-276, March.
    6. Neuenkirch, A. & Tindel, S. & Unterberger, J., 2010. "Discretizing the fractional Lévy area," Stochastic Processes and their Applications, Elsevier, vol. 120(2), pages 223-254, February.
    7. Alexandra Chronopoulou & Samy Tindel, 2013. "On inference for fractional differential equations," Statistical Inference for Stochastic Processes, Springer, vol. 16(1), pages 29-61, April.
    8. Peter Kloeden & Andreas Neuenkirch & Raffaella Pavani, 2011. "Multilevel Monte Carlo for stochastic differential equations with additive fractional noise," Annals of Operations Research, Springer, vol. 189(1), pages 255-276, September.
    9. Bardina, X. & Nourdin, I. & Rovira, C. & Tindel, S., 2010. "Weak approximation of a fractional SDE," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 39-65, January.
    10. Song, Jian & Tindel, Samy, 2022. "Skorohod and Stratonovich integrals for controlled processes," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 569-595.
    11. Passeggeri, Riccardo, 2020. "On the signature and cubature of the fractional Brownian motion for H>12," Stochastic Processes and their Applications, Elsevier, vol. 130(3), pages 1226-1257.
    12. Qi Feng & Jianfeng Zhang, 2021. "Cubature Method for Stochastic Volterra Integral Equations," Papers 2110.12853, arXiv.org, revised Jul 2023.

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