On the Distribution of Explosion Time of Stochastic Differential Equations

TL;DR

This paper extends criteria for finite-time blow-up in stochastic differential equations driven by Brownian motion and provides methods to determine the distribution of explosion times.

Contribution

It introduces an extended Osgood criterion applicable to nonautonomous SDEs with additive Wiener noise and offers a way to compute explosion time distributions.

Findings

Extended Osgood criterion for stochastic equations.

Method to determine explosion time distribution.

Applicable to nonautonomous SDEs with Wiener noise.

Abstract

In this paper we use the It\^o'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.