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Comparison theorems for stochastic differential equations in finite and infinite dimensions

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  • Geiß, Christel
  • Manthey, Ralf

Abstract

We prove comparison theorems for systems of ordinary stochastic differential equations as well as for stochastic partial differential equations.

Suggested Citation

  • Geiß, Christel & Manthey, Ralf, 1994. "Comparison theorems for stochastic differential equations in finite and infinite dimensions," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 23-35, September.
    • Handle: RePEc:eee:spapps:v:53:y:1994:i:1:p:23-35
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    Citations

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    Cited by:

    1. Wu, Zhen & Xu, Mingyu, 2009. "Comparison theorems for forward backward SDEs," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 426-435, February.
    2. Damir Filipovi'c & Sander Willems, 2018. "A Term Structure Model for Dividends and Interest Rates," Papers 1803.02249, arXiv.org, revised May 2020.
    3. Rajasekar, S.P. & Pitchaimani, M., 2019. "Qualitative analysis of stochastically perturbed SIRS epidemic model with two viruses," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 207-221.
    4. Zhang, Na & Jia, Guangyan, 2013. "Stochastic monotonicity and order-preservation for a type of nonlinear semigroups," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 422-429.
    5. Damir Filipović & Sander Willems, 2020. "A term structure model for dividends and interest rates," Mathematical Finance, Wiley Blackwell, vol. 30(4), pages 1461-1496, October.
    6. Wang, Tianxiao & Yong, Jiongmin, 2015. "Comparison theorems for some backward stochastic Volterra integral equations," Stochastic Processes and their Applications, Elsevier, vol. 125(5), pages 1756-1798.
    7. Ding, Xiaodong & Wu, Rangquan, 1998. "A new proof for comparison theorems for stochastic differential inequalities with respect to semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 78(2), pages 155-171, November.
    8. Mukama, Denis Sospeter & Ghani, Mohammad & Mbalawata, Isambi Sailon, 2023. "Persistence, Extinction, and boundedness in pth moment of hybrid stochastic logistic systems by delay feedback control based on discrete-time observation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 210(C), pages 661-677.
    9. Nguyen, Dang H. & Nguyen, Nhu N. & Yin, George, 2020. "General nonlinear stochastic systems motivated by chemostat models: Complete characterization of long-time behavior, optimal controls, and applications to wastewater treatment," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4608-4642.

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