Accelerated Spatial Approximations for Time Discretized Stochastic Partial Differential Equations

Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations

We describe and analyze two numerical methods for a linear elliptic problem with stochastic coefficients and homogeneous Dirichlet boundary conditions. Here the aim of the computations is to approximate statistical moments of the solution, and, in particular, we give a priori error estimates for the computation of the expected value of the solution. The first method generates independent identi...

Spatial Stochastic Models Generated by Nested Stochastic Partial Differential Equations

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Matérn fields and a wide family of fields with oscillating covariance functions. Non-stationary covariance models are obtained by spatially varying the pa...

global results on some nonlinear partial differential equations for direct and inverse problems

در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...

Stochastic Partial Differential Equations

Time-homogeneous Affine State Processes for Stochastic Partial Differential Equations

The goal of this paper is to clarify for which starting points the state processes of a stochastic partial differential equation with an affine realization are time-homogeneous. We will illustrate our results by means of the HJMM equation from mathematical finance.