Weak Numerical Schemes for Stochastic Differential Equations in Geophysics

Abstract

In the past few decades, scientists studying the partial differential equations used to describe the dynamics of the atmosphere and oceans in weather and climate models have become increasingly interested in using stochastic differential equations (SDEs) in the attempt to include effects and interactions which take place on scales which their discretizations might otherwise ignore. I will discuss certain issues that arise when attempting to integrate SDEs numerically. In addition, in many cases, geophysicists have existing numerical models that they have developed to approximate the solution to certain nonstochastic differential equations, which they would like to modify by the addition of stochastic terms. I will discuss some examples in which this has been attempted.