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A Variational Characterization of the Risk-Sensitive Average Reward for Controlled Diffusions on $\mathbb{R}^d$
- Source :
- SIAM Journal on Control and Optimization. 58:3785-3813
- Publication Year :
- 2020
- Publisher :
- Society for Industrial & Applied Mathematics (SIAM), 2020.
-
Abstract
- 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.<br />Comment: 29 pages
- Subjects :
- 0209 industrial biotechnology
Primary 60J60, Secondary 60J25, 35K59, 35P15, 60F10
Control and Optimization
Applied Mathematics
Probability (math.PR)
010102 general mathematics
02 engineering and technology
Characterization (mathematics)
Risk sensitive
01 natural sciences
Mathematics - Analysis of PDEs
020901 industrial engineering & automation
Optimization and Control (math.OC)
FOS: Mathematics
Applied mathematics
0101 mathematics
Mathematics - Optimization and Control
Mathematics - Probability
Analysis of PDEs (math.AP)
Mathematics
Subjects
Details
- ISSN :
- 10957138 and 03630129
- Volume :
- 58
- Database :
- OpenAIRE
- Journal :
- SIAM Journal on Control and Optimization
- Accession number :
- edsair.doi.dedup.....aef79cf0c9c101d1aae587885fcf9708