Large deviation principle for diffusion processes under a sublinear expectation
type: Item
instance of: scholarly article
title: Large deviation principle for diffusion processes under a sublinear expectation
zbMATH Open document ID: 1284.60058
author: Jie Xiong
author: Zengjing Chen
published in: Science China. Mathematics
publication date: 2013-01-28T00:00:00Z
review text: The authors consider the one-dimensional stochastic differential equation (SDE) \(dx^{\varepsilon}_t=b(x^{\varepsilon}_t)dt +\sigma(x^{\varepsilon}_t)dW(t)\) on \([0,T]\), where \(W\) is the standard Brownian motion on \((\Omega,F,\operatorname{P})\). On \((\Omega,F)\), they define for each \(k \geq 0\) a class of probability measures \({\mathcal{P}}_k\) containing \(\operatorname{P}\) and the associated sub-linear probability \(\operatorname{P}_k\) by \(\operatorname{P}_k(A):=\sup_{Q \in {\mathcal{P}}_k} \operatorname{E}_Q 1_A\). The authors show how \(\operatorname{P}_k\) can be defined via an associated backward SDE. They establish a large deviation property for \(\operatorname{P}_k(X_T \in .)\) similar to the classical case using the Laplace principle approach.
Mathematics Subject Classification ID: 60F10
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 6131941
zbMATH Keywords: large deviation principle
zbMATH Keywords: backward stochastic differential equation
zbMATH Keywords: \(g\)-expectation
zbMATH Keywords: Laplace principle
reviewed by: Michael Scheutzow
MaRDI profile type: Publication
full work available at URL: s11425-012-4518-4
OpenAlex ID: W2108060696
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DOI: 10.1007/S11425-012-4518-4
description: scientific article; zbMATH DE number 6131941