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

Scott Robertson and Hao Xing

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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.

Keywords: semilinear equation; quadratic growth gradient; large time behaviour; ergodic equation (search for similar items in EconPapers)
JEL-codes: F3 G3 (search for similar items in EconPapers)
Date: 2015-01-13
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Citations: View citations in EconPapers (4)

Published in SIAM Journal on Control and Optimization, 13, January, 2015, 53(1), pp. 185-212. ISSN: 0363-0129

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