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Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient

Robertson, Scott and Xing, Hao (2015) Large time behavior of solutions to semi-linear equations with quadratic growth in the gradient. SIAM Journal on Control and Optimization, 53 (1). pp. 185-212. ISSN 0363-0129

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Identification Number: 10.1137/13094311X

Abstract

This paper studies the large time behavior of solutions to semi-linear Cauchy problems with quadratic nonlinearity in gradients. The Cauchy problem considered has a general state space and may degenerate on the boundary of the state space. Two types of large time behavior are obtained: i) pointwise convergence of the solution and its gradient; ii) convergence of solutions to associated backward stochastic di�erential equations. When the state space is Rd or the space of positive de�nite matrices, both types of convergence are obtained under growth conditions on coe�cients. These large time convergence results have direct applications in risk sensitive control and long term portfolio choice problems.

Item Type: Article
Official URL: http://epubs.siam.org/loi/sjcodc
Additional Information: © 2014 SIAM
Divisions: Statistics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Sets: Departments > Statistics
Date Deposited: 22 Dec 2014 12:40
Last Modified: 20 Feb 2019 11:12
Projects: DMS-1312419
Funders: National Science Foundation
URI: http://eprints.lse.ac.uk/id/eprint/60578

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