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Almost sure explosion of solutions to stochastic differential equations

Author

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  • Chow, Pao-Liu
  • Khasminskii, Rafail

Abstract

This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given.

Suggested Citation

  • Chow, Pao-Liu & Khasminskii, Rafail, 2014. "Almost sure explosion of solutions to stochastic differential equations," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 639-645.
    • Handle: RePEc:eee:spapps:v:124:y:2014:i:1:p:639-645
    DOI: 10.1016/j.spa.2013.09.006
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    Cited by:

    1. Dan Pirjol & Lingjiong Zhu, 2019. "Explosion in the quasi-Gaussian HJM model," Papers 1908.07102, arXiv.org.
    2. Bezborodov, Viktor & Di Persio, Luca & Kuchling, Peter, 2024. "Explosion and non-explosion for the continuous-time frog model," Stochastic Processes and their Applications, Elsevier, vol. 171(C).
    3. Linna Liu & Feiqi Deng & Boyang Qu & Yanhong Meng, 2022. "Fundamental Properties of Nonlinear Stochastic Differential Equations," Mathematics, MDPI, vol. 10(15), pages 1-18, July.
    4. Jianhai Bao & Chenggui Yuan, 2016. "Blow-up for Stochastic Reaction-Diffusion Equations with Jumps," Journal of Theoretical Probability, Springer, vol. 29(2), pages 617-631, June.
    5. Dan Pirjol & Lingjiong Zhu, 2018. "Explosion in the quasi-Gaussian HJM model," Finance and Stochastics, Springer, vol. 22(3), pages 643-666, July.

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