Gradient type noises II – Systems of stochastic partial differential equations

Gradient type noises II – Systems of stochastic partial differential equations

The present paper is the second and main part of a study of partial differential equations under the influence of noisy perturbations. Existence and uniqueness of function solutions in the mild sense are obtained for a class of deterministic linear and semilinear parabolic boundary initial value problems. If the noise data are random, the results may be seen as a pathwise approach to SPDE’s. Fo...

Stochastic Partial Differential Equations

Numerical Approximation of Some Linear Stochastic Partial Differential Equations Driven by Special Additive Noises

This paper is concerned with the numerical approximation of some linear stochastic partial differential equations with additive noises. A special representation of the noise is considered, and it is compared with general representations of noises in the infinite dimensional setting. Convergence analysis and error estimates are presented for the numerical solution based on the standard finite di...

Gradient Type Noises I - Partial and Hybrid Integrals

The final objective of our study is to propose a finite dimensional approach to systems of parabolic partial differential equations perturbed by low order noises of Brownian or fractional Brownian type. The present paper is the preparatory first part, where we introduce partial pathwise integrals over D and (a, b) × D, where D is a smooth bounded domain in R. Corresponding stochastic versions a...

Conditional distributions, exchangeable particle systems, and stochastic partial differential equations

Stochastic partial differential equations (SPDEs) whose solutions are probabilitymeasure-valued processes are considered. Measure-valued processes of this type arise naturally as de Finetti measures of infinite exchangeable systems of particles and as the solutions for filtering problems. In particular, we consider a model of asset price determination by an infinite collection of competing trad...