A Sobolev Space Theory for Time-Fractional Stochastic Partial Differential Equations Driven by Levy Processes

초록

We present an L p-theory ( p >= 2) for semi-linear time-fractional stochastic partial differential equations driven by Levy processes of the type [GRAPHICS] . given with nonzero initial data. Here,partial derivative(alpha)(t) and partial derivative(beta)(t) t are the Caputo fractional derivatives, 0 < alpha < 2, beta< alpha + 1/ p, and {Z(t)(k) : k = 1, 2,...} is a sequence of independentLevy processes. The coefficients are random functions depending on (t, x). We prove the uniqueness and existence results in Sobolev spaces and obtain the maximal regularity of the solution. As an application, we also obtain an L-p-regularity theory of the equation [GRAPHICS] .

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