Stochastic De Giorgi iteration and regularity of stochastic partial differential equations

Stochastic Partial Differential Equations

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.

Introduction to the Theory of Stochastic Differential Equations and Stochastic Partial Differential Equations

1 Some Basic Concepts in Probability Theory 2 1.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Several Different Notions of Convergence of Random Variables . . . . . . . . . 3 1.3 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Stochastic Processes . . . . . . . . . . . . . . . . . . . . . . ....

Applications of Stochastic Partial Differential Equations

s of the talks Robert Adler, Technion-Israel Institute of Technology, Israel On quantifying shape, with two applications to stochastic processes I shall discuss some classical Integral and Differential Geometric ways to classify shape, and describe 1. A new class of results about the excursion sets of smooth random fields which uses them. 2. An application of these classifiers to the study of t...

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...