In this paper, we study a partial differential equation (PDE) framework for option pricing where the underlying factors exhibit stochastic correlation, with an emphasis on computation. We derive a multi-dimensional time-dependent PDE for the corresponding pricing problem, and present a numerical PDE solution. We prove a stability result, and study numerical issues regarding the boundary conditi...

We consider a class of parabolic semi-linear stochastic partial differential equations driven by space-time white noise on a compact space interval. Our aim is to obtain precise asymptotics of the transition times between metastable states. A version of the so-called Eyring-Kramers Formula is proven in an infinite dimensional setting. The proof is based on a spatial finite difference discretiza...

In this paper, we establish a Stroock-Varadhan support theorem for the global mild solution to a d (d ≤ 3)-dimensional stochastic Cahn-Hilliard partial differential equation driven by a space-time white noise.

By using functional integral methods we determine new types of differential constraints satisfied by the joint probability density function of stochastic solutions to the wave equation subject to uncertain boundary and initial conditions. These differential constraints involve unusual limit partial differential operators and, in general, they can be grouped into two main classes: the first one ...

The goal of this paper is to clarify when a semilinear stochastic partial differential equation driven by Lévy processes admits an affine realization. Our results are accompanied by several examples arising in natural sciences and economics.

We approximate the solution of a quasilinear stochastic partial differential equation driven by fractional Brownian motion BH(t); H ∈ (0, 1), which was calculated via fractional White Noise calculus, see [5].

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiencyand convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partia...

Abstract. We study the Cauchy problem for a semilinear stochastic partial differential equation driven by a finite-dimensional Wiener process. In particular, under the hypothesis that all the coefficients are sufficiently smooth and have bounded derivatives, we consider the equation in the context of power scale generated by a strongly elliptic differential operator. Application of semigroup ar...

Stochastic models of some aspects of the electrical activity in the nervous system at the cellular level are developed. In particular, models of the subthreshold behavior of the membrane potential of neurons ar~ consid~r~d alon& ~ith the problem of parameter estimation of physiologically meaningful parameters of the developed models. Both ordinary and partial stochastic differential equation mo...

A new class of random partial differential equations of parabolic type is considered where the stochastic term consists in an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a prob...