Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
10525857 | Statistics & Probability Letters | 2011 | 8 Pages |
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 Xt=a+â«0tb(Xs)ds+g(t),tâ¥0. Here, g is a measurable function such that lim suptââ(inf0â¤hâ¤1g(t+h))=â, 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 â«â
âdsb(s)<â. 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
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Jorge A. León, José Villa,