Distribution of the time to explosion for one-dimensional diffusions

By Ioannis Karatzas, J. Ruf. Probability theory and related fields, 2013

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We study the distribution of the time to explosion for one-dimensional diffusions. We relate this question to the computation of expectations of suitable nonnegative local martingales. Moreover, we characterize the distribution function of the time to explosion as the minimal solution to a certain Cauchy problem for an appropriate parabolic differential equation; this leads to alternative characterizations of Feller’s criterion for explosions. We discuss in detail several examples for which it is possible to obtain analytic expressions for the corresponding distribution of the time to explosion, using the methodologies developed in the paper.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/eff5227d21bf743e9f9640e1e11f2962c4ec235e