Theory of Probability and Mathematical Statistics
Stochastic heat equation with piecewise constant coefficients and generalized fractional type noise
M. Zili, E. Zougar
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Abstract: We investigate a new stochastic partial differential equation with second order elliptic operator in divergence form, having a piecewise constant diffusion coefficient with two points of discontinuity, and driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. Such equation could be used in mathematical modeling of diffusion phenomena in medium consisting of three kinds of materials and undergoing stochastic perturbations. We focus our attention on the particular case when the noise behaves as a generalized fractional Brownian motion in time.
Keywords: Stochastic partial differential equations, piecewise constant coefficients, generalized fractional Brownian motion, covariance measure structure, Wiener integral
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