Displaying similar documents to “On some fractional stochastic integrodifferential equations in Hilbert space.”

Stochastic evolution equations driven by Liouville fractional Brownian motion

Zdzisław Brzeźniak, Jan van Neerven, Donna Salopek (2012)

Czechoslovak Mathematical Journal

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Let H be a Hilbert space and E a Banach space. We set up a theory of stochastic integration of ℒ ( H , E ) -valued functions with respect to H -cylindrical Liouville fractional Brownian motion with arbitrary Hurst parameter 0 < β < 1 . For 0 < β < 1 2 we show that a function Φ : ( 0 , T ) → ℒ ( H , E ) is stochastically integrable with respect to an H -cylindrical Liouville fractional Brownian motion if and only if it is stochastically integrable with respect to an H -cylindrical fractional Brownian motion. We apply our results to stochastic...

Stochastic Solution of a KPP-Type Nonlinear Fractional Differential Equation

Cipriano, F., Ouerdiane, H., Vilela Mendes, R. (2009)

Fractional Calculus and Applied Analysis

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Mathematics Subject Classification: 26A33, 76M35, 82B31 A stochastic solution is constructed for a fractional generalization of the KPP (Kolmogorov, Petrovskii, Piskunov) equation. The solution uses a fractional generalization of the branching exponential process and propagation processes which are spectral integrals of Levy processes.

A note on maximal inequality for stochastic convolutions

Erika Hausenblas, Jan Seidler (2001)

Czechoslovak Mathematical Journal

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Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution ∫ 0 t S ( t - s ) ψ ( s ) d W ( s ) driven by a Wiener process W in a Hilbert space in the case when the semigroup S ( t ) is of contraction type.