In this paper we describe a general framework for deriving modified equations for stochastic differential equations with respect to weak convergence. Modified equations are deri...
We study spectral properties of certain families of linear second-order differential operators arising from linear stochastic differential equations. We construct a basis in the Hi...
We study the pathwise (strong) approximation of scalar stochastic differential equations with respect to the global error in the L2-norm. For equations with additive noise we estab...
Evolution equations have proven to be useful in tracking fine to coarse features in a single level curve and/or in an image. In this paper, we give a stochastic insight to a speci...
We study properties of solutions to fully nonlinear versions of the standard Black– Scholes partial differential equation. These equations have been introduced in financial mat...