We study parameter estimation problem for diagonalizable stochastic partial differential equations driven by a multiplicative fractional noise with any Hurst parameter H ∈ (0, 1). Two classes of estimators are investigated: traditional maximum likelihood type estimators, and a new class called closed-form exact estimators. Finally the general results are applied to stochastic heat equation driv...

In this paper we obtain a Feynman-Kac formula for the solution of a fractional stochastic heat equation driven by fractional noise. One of the main difficulties is to show the exponential integrability of some singular nonlinear functionals of symmetric stable Lévy motion. This difficulty will be overcome by a technique developed in the framework of large deviation. This Feynman-Kac formula is ...

The fundamental concern of this article has been to apply the residual power series method (RPSM) effectively to determine of the unknown spacewise dependent coefficient in the time fractional heat equation in the Caputo sense with over measured data. First, the fractional power series solution of inverse problem of unknown spacewise dependent coefficient is obtained by residual power series me...

Abstract In this article we present a quantitative central limit theorem for the stochastic fractional heat equation driven by general Gaussian multiplicative noise, including cases of space–time white noise and white-colored with spatial covariance given Riesz kernel or bounded integrable function. We show that average over ball radius R converges, as tends to infinity, after suitable renormal...

The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). The boundary value problem for the fractional heat equation is solved by means of the Caputo differintegration operator D ∗ of order 0 < α ≤ 1 and the Laplace transform. The solution is obtained ...

Abstract: We consider three level difference replacements of parabolic equations focusing on the heat equation in two space dimensions. Through a judicious splitting of the approximation, the scheme qualifies as an alternating direction implicit (ADI) method. Using the well known fact of the parabolic-elliptic correspondence, we shall derive a two stage iterative procedure employing a fractiona...

In this article we consider the stochastic heat equation in [0, T ]× Rd, driven by a sequence (β)k of i.i.d. fractional Brownian motions of index H > 1/2 and random multiplication functions (g)k. The stochastic integrals are of Hitsuda-Skorohod type and the solution is interpreted in the weak sense. Using Malliavin calculus techniques, we prove the existence and uniqueness of the solution in a ...

We investigate the fractional heat equation with translation in both time and position different orders. As examples, we consider a rod an α -disk initial constant temperature discuss their cooling processes examined formalism.