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Stochastic evolution equations and related measure processes

Author

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  • Dawson, D. A.

Abstract

Basic results on stochastic differential equations in Hilbert and Banach space, linear stochastic evolution equations and some classes of nonlinear stochastic evolution equations are reviewed. The emphasis is on equations relevant to the study of spacetime stochastic processes. In particular the class of measure processes, the continuous analogs of spacetime population processes, is studied in detail.

Suggested Citation

  • Dawson, D. A., 1975. "Stochastic evolution equations and related measure processes," Journal of Multivariate Analysis, Elsevier, vol. 5(1), pages 1-52, March.
    • Handle: RePEc:eee:jmvana:v:5:y:1975:i:1:p:1-52
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    Citations

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    Cited by:

    1. Mytnik, Leonid & Neuman, Eyal, 2015. "Pathwise uniqueness for the stochastic heat equation with Hölder continuous drift and noise coefficients," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3355-3372.
    2. Ethier, S. N. & Krone, Stephen M., 1995. "Comparing Fleming-Viot and Dawson-Watanabe processes," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 171-190, December.
    3. Ubøe, Jan & Zhang, Tusheng, 1995. "A stability property of the stochastic heat equation," Stochastic Processes and their Applications, Elsevier, vol. 60(2), pages 247-260, December.
    4. Goncharuk, Nataliya Yu. & Kotelenez, Peter, 1998. "Fractional step method for stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 73(1), pages 1-45, January.
    5. Mandler, Christian & Overbeck, Ludger, 2022. "A functional Itō-formula for Dawson–Watanabe superprocesses," Stochastic Processes and their Applications, Elsevier, vol. 144(C), pages 202-228.
    6. Rémillard, Bruno & Vaillancourt, Jean, 2014. "On signed measure valued solutions of stochastic evolution equations," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 101-122.
    7. Valentin Tissot-Daguette, 2023. "Occupied Processes: Going with the Flow," Papers 2311.07936, arXiv.org, revised Dec 2023.

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