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arXiv · 1903.08346

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

Ari Arapostathis·Anup Biswas·Vivek S. Borkar·K. Suresh Kumar
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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.

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Ari Arapostathis, Anup Biswas, Vivek S. Borkar, K. Suresh Kumar. 2019-03-20. A variational characterization of the risk-sensitive average reward for controlled diffusions on $\mathbb{R}^d$. https://doi.org/10.1137/20m1329202

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