An Osgood criterion for integral equations with applications to stochastic differential equations with an additive noise

Jorge A. León and José Villa

Statistics & Probability Letters, 2011, vol. 81, issue 4, 470-477

Abstract: In this paper we use a comparison theorem for integral equations to show that the classical Osgood criterion can be applied to solutions of integral equations of the form Here, g is a measurable function such that and b is a positive and non-decreasing function. Namely, we will see that the solution X explodes in finite time if and only if . As an example, we use the law of the iterated logarithm to see that the bifractional Brownian motion and some increasing self-similar Markov processes satisfy the above condition on g. In other words, g can represent the paths of these processes.

Keywords: Bifractional; Brownian; motion; Comparison; theorem; Feller; test; Osgood; criterion (search for similar items in EconPapers)
Date: 2011
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