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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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 |
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Official URL: | http://epubs.siam.org/loi/sjcodc |
Additional Information: | © 2014 SIAM |
Divisions: | Statistics |
Subjects: | H Social Sciences > HG Finance Q Science > QA Mathematics |
Date Deposited: | 22 Dec 2014 12:40 |
Last Modified: | 14 Sep 2024 06:44 |
Projects: | DMS-1312419 |
Funders: | National Science Foundation |
URI: | http://eprints.lse.ac.uk/id/eprint/60578 |
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