Explosion time in stochastic differential equations with small diffusion
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We consider solutions of a one dimensional stochastic differential equations that explode in finite time. We prove that, under suitable hypotheses, the explosion time converges almost surely to the one of the ODE governed by the drift term when the diffusion coefficient approaches zero.
CitationGroisman, P., & Rossi, J. D. (2007). Explosion time in stochastic differential equations with small diffusion. Electronic Journal of Differential Equations, 2007(140), pp. 1-9.
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