Distribution of the time to explosion for one-dimensional diffusions

• 成果类型: Article
• 署名作者: Karatzas, Ioannis; Ruf, Johannes
• 署名单位: Columbia University; University of London; University College London
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-015-0625-9
• 发表日期: 2016
• 页码: 1027-1069
• 关键词: martingales

摘要

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.