Displaying similar documents to “Explicit solutions of some fractional partial differential equations via stable subordinators.”

Fractional Fokker-Planck-Kolmogorov type Equations and their Associated Stochastic Differential Equations

Hahn, Marjorie, Umarov, Sabir (2011)

Fractional Calculus and Applied Analysis

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MSC 2010: 26A33, 35R11, 35R60, 35Q84, 60H10 Dedicated to 80-th anniversary of Professor Rudolf Gorenflo There is a well-known relationship between the Itô stochastic differential equations (SDEs) and the associated partial differential equations called Fokker-Planck equations, also called Kolmogorov equations. The Brownian motion plays the role of the basic driving process for SDEs. This paper provides fractional generalizations of the triple relationship between the driving...

The fractional mixed fractional brownian motion and fractional brownian sheet

Charles El-Nouty (2007)

ESAIM: Probability and Statistics

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We introduce the fractional mixed fractional Brownian motion and fractional Brownian sheet, and investigate the small ball behavior of its sup-norm statistic. Then, we state general conditions and characterize the sufficiency part of the lower classes of some statistics of the above process by an integral test. Finally, when we consider the sup-norm statistic, the necessity part is given by a second integral test.