A new Markov selection procedure for degenerate diffusions
type: Item
instance of: scholarly article
title: A new Markov selection procedure for degenerate diffusions
zbMATH Open document ID: 1214.60022
author: Vivek Borkar
author: K. Suresh Kumar
published in: Journal of Theoretical Probability
publication date: 2010-10-13T00:00:00Z
review text: The authors consider the \(d\)-dimensional stochastic differential equation \[ dX(t) = m(X(t))dt + \sigma(X(t))dW(t),\;\;X(0)=x, \] and the continuous viscosity solutions to the corresponding backward Kolmogorov equation for various time intervals and terminal conditions. Attention is paid to the limits as the noise decreases to zero, and a unique limit is found for certain conditions on \(m\) and \(\sigma\). A unique choice of limiting transition laws satisfying the Chapman-Kolmogorov equations results, and the canonical construction of a Markov process consistent with the given s.d.e.\ is hence obtained.
Mathematics Subject Classification ID: 60H10
Mathematics Subject Classification ID: 60J25
Mathematics Subject Classification ID: 34F05
Mathematics Subject Classification ID: 35K65
zbMATH DE Number: 5799411
zbMATH Keywords: degenerate diffusions
zbMATH Keywords: Feller process
zbMATH Keywords: Markov selection: backward Kolmogorov equation
zbMATH Keywords: viscosity solution
zbMATH Keywords: small noise limit
reviewed by: Andrew Dale
MaRDI profile type: Publication
full work available at URL: s10959-009-0242-6
OpenAlex ID: W2045282631
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DOI: 10.1007/S10959-009-0242-6
description: scientific article; zbMATH DE number 5799411