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

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  • León, Jorge A.
  • Villa, José

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.

Suggested Citation

  • León, Jorge A. & Villa, José, 2011. "An Osgood criterion for integral equations with applications to stochastic differential equations with an additive noise," Statistics & Probability Letters, Elsevier, vol. 81(4), pages 470-477, April.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:4:p:470-477
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    References listed on IDEAS

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    1. Nualart, David & Ouknine, Youssef, 2002. "Regularization of differential equations by fractional noise," Stochastic Processes and their Applications, Elsevier, vol. 102(1), pages 103-116, November.
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