Multiscale Stochastic Reaction–Diffusion Algorithms Combining Markov Chain Models with Stochastic Partial Differential Equations

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...

Stochastic Partial Differential Equations

Model, Identification & Analysis of Complex Stochastic Systems: Applications in Stochastic Partial Differential Equations and Multiscale Mechanics

xi 1 Chapter 1: Introduction 1 1.1 Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Notation and Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Chapter 2: Asymptotic Distribution for Polynomial Chaos Representation from Data 5 2.1 Motivation and Problem Description . . . . . . . . . . . . . . . . . . . . . . ....

Multiscale Analysis of Stochastic Delay Differential Equations

We apply multi-scale analysis to stochastic delay-differential equations, deriving approximate stochastic equations for the amplitudes of oscillatory solutions near critical delays of deterministic systems. Such models are particularly sensitive to noise when the system is near a critical point, which marks a transition to sustained oscillatory behavior in the deterministic system. In particula...

Fast Algorithms for the Solution of Stochastic Partial Differential Equations

Title of dissertation: FAST ALGORITHMS FOR THE SOLUTION OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS Christopher W. Miller, Doctor of Philosophy, 2012 Dissertation directed by: Professor Howard Elman Department of Computer Science Institute for Advanced Computer Studies We explore the performance of several algorithms for the solution of stochastic partial differential equations including the s...