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Theory of Probability and Mathematical Statistics



Exact variations for stochastic heat equations with piecewise constant coefficients and application to parameter estimation

M. Zili, E. Zougar

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Abstract: We expand the quartic variations in time and the quadratic variations in space of the solution to a stochastic partial differential equation with piecewise constant coefficients. Both expansions allow us to deduce an estimation method of the parameters appearing in the equation.

Keywords: Quartic and quadratic variations, stochastic partial differential equations, discontinuity, integration techniques, special functions, estimation of parameters.

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