A variational characterization of the risk-sensitive average reward for controlled diffusions on $\mathbb{R}^d$

Autor:	Arapostathis, Ari, Biswas, Anup, Borkar, Vivek S., Kumar, K. Suresh
Rok vydání:	2019
Předmět:	Mathematics - Analysis of PDEs Mathematics - Optimization and Control Mathematics - Probability Primary 60J60 Secondary 60J25 35K59 35P15 60F10
Zdroj:	SIAM Journal on Control and Optimization 58 (2020), no. 6, 3785-3813
Druh dokumentu:	Working Paper
DOI:	10.1137/20M1329202
Popis:	We address the variational formulation of the risk-sensitive reward problem for non-degenerate diffusions on $\mathbb{R}^d$ controlled through the drift. We establish a variational formula on the whole space and also show that the risk-sensitive value equals the generalized principal eigenvalue of the semilinear operator. This can be viewed as a controlled version of the variational formulas for principal eigenvalues of diffusion operators arising in large deviations. We also revisit the average risk-sensitive minimization problem and by employing a gradient estimate developed in this paper, we extend earlier results to unbounded drifts and running costs. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1903.08346 Zobrazit plný text záznamu View this record from Arxiv