Some SDEs with distributional drift. I: General calculus
type: Item
instance of: scholarly article
title: Some SDEs with distributional drift. I: General calculus
zbMATH Open document ID: 1054.60069
author: Francesco Russo
author: Jochen Wolf
author: Franco Flandoli
published in: Osaka Journal of Mathematics
publication date: 2003-11-10T00:00:00Z
review text: Let \[ X_t=x_0+\int^t_0\sigma(X_s)\,dW_s+ \int^t_0b'(X_s)\,ds, \] where \(b,\sigma\) \((\sigma>0)\) are continuous functions, be a stochastic differential equation and \[ Lf=\frac{\sigma^2} {2}f''+b'f'' \] be an operator associated with \(X\). The authors cosider a martingale problem assiociated with \(L\). They show that the solution of the martingale problem will solve some stochastic differential equation. They also prove the theorem on the Dirichlet-Fukushima structure of \(f(X)\) for \(f\in W_{\text{loc}}^{1,2}\) \((f\) absolutely continuous with \(f'\) square integrable on compact subsets).
Mathematics Subject Classification ID: 60H20
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 47D07
Mathematics Subject Classification ID: 47N30
zbMATH DE Number: 2002270
zbMATH Keywords: stochastic differential equation
zbMATH Keywords: martingale problem
zbMATH Keywords: Dirichlet-Fukushima structure
reviewed by: Maria Stolarczyk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2002270