Fractional relaxation equations and Brownian crossing probabilities of a random boundary

Details Fractional relaxation equations and Brownian crossing probabilities of a random boundary Fractional relaxation equations and Brownian crossing probabilities of a random boundary

2011-07-13

arxiv.org/abs/1107.2515v1

Mathematics

Probability

27 pages

Scientific paper

We analyze here different forms of fractional relaxation equations of order {\nu}\in(0,1) and we derive their solutions both in analytical and in probabilistic forms. In particular we show that these solutions can be expressed as crossing probabilities of random boundaries by various types of stochastic processes, which are all related to the Brownian motion B. In the special case {\nu}=1/2, the fractional relaxation is proved to coincide with Pr{sup_{0\leqs\leqt} B(s)

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