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SIAMSC
2011
133views more  SIAMSC 2011»
12 years 11 months ago
On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
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...
K. C. Zygalakis
SIAMCO
2000
99views more  SIAMCO 2000»
13 years 4 months ago
Spectral Analysis of Fokker--Planck and Related Operators Arising From Linear Stochastic Differential Equations
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...
Daniel Liberzon, Roger W. Brockett
MOC
2000
76views more  MOC 2000»
13 years 4 months ago
Optimal approximation of stochastic differential equations by adaptive step-size control
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...
Norbert Hofmann, Thomas Müller-Gronbach, Klau...
ICIP
2000
IEEE
14 years 6 months ago
Feature-Preserving Flows: A Stochastic Differential Equation's View
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...
Gozde B. Unal, Hamid Krim, Anthony J. Yezzi
SIAMCO
2011
12 years 11 months ago
Nonlinear Black-Scholes Equations in Finance: Associated Control Problems and Properties of Solutions
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...
Rüdiger Frey, Ulrike Polte