On the Distribution of Explosion Time of Stochastic Differential Equations

2013/05/13 by Jorge A. Leòn, León, Jorge A., Liliana Peralta Hernández +3 · 1 citation
Economics, Econometrics and Finance · Physics and Astronomy · #60H10 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Primary 45R05 #Probability (math.PR) #Secondary 49K20 #Stochastic processes and financial applications #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.1305.2870

openalex publication_date 2013/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we use the Itô's formula and comparison theorems to study the blow-up in finite time of stochastic differential equations driven by a Brownian motion. In particular, we obtain an extension of Osgood criterion, which can be applied to some nonautonomous stochastic differential equations with additive Wiener integral noise. In most cases we are able to provide with a method to figure out the distribution of the explosion time of the involved equation.

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