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Linear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion

In: Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems

Author

Listed:
  • B. Pasik-Duncan

    (University of Kansas)

  • T. E. Duncan

    (University of Kansas)

  • B. Maslowski

    (Czech Academy of Sciences)

Abstract

A solution is obtained for a linear stochastic equation in a Hilbert space with a fractional Brownian motion. The Hurst parameter for the fractional Brownian motion is not restricted. Sample path properties of the solution are obtained that depend on the Hurst parameter. An example of a stochastic partial differential equation is given.

Suggested Citation

  • B. Pasik-Duncan & T. E. Duncan & B. Maslowski, 2006. "Linear Stochastic Equations in a Hilbert Space with a Fractional Brownian Motion," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 201-221, Springer.
  • Handle: RePEc:spr:isochp:978-0-387-33815-6_11
    DOI: 10.1007/0-387-33815-2_11
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    Citations

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    Cited by:

    1. Zhi Li & Litan Yan, 2019. "Ergodicity and Stationary Solution for Stochastic Neutral Retarded Partial Differential Equations Driven by Fractional Brownian Motion," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1399-1419, September.
    2. Pavel Kříž & Leszek Szała, 2020. "The Combined Estimator for Stochastic Equations on Graphs with Fractional Noise," Mathematics, MDPI, vol. 8(10), pages 1-21, October.
    3. Zhang, Yinghan & Yang, Xiaoyuan, 2015. "Fractional stochastic Volterra equation perturbed by fractional Brownian motion," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 20-36.
    4. Issoglio, E. & Riedle, M., 2014. "Cylindrical fractional Brownian motion in Banach spaces," Stochastic Processes and their Applications, Elsevier, vol. 124(11), pages 3507-3534.

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