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semilinear differential equations

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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On the policy improvement algorithm for ergodic risk-sensitive control
Part of
Ari Arapostathis, Anup Biswas, Somnath Pradhan
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 151 / Issue 4 / August 2021

Published online by Cambridge University Press:

02 September 2020, pp. 1305-1330

Print publication:

August 2021
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In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.