A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$

Ari Arapostathis; Anup Biswas

doi:10.1137/18m1218704

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arXiv · 1810.01180

A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$

Ari Arapostathis·Anup Biswas

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Abstract

We address the variational problem for the generalized principal eigenvalue on $\mathbb{R}^d$ of linear and semilinear elliptic operators associated with nondegenerate diffusions controlled through the drift. We establish the Collatz-Wielandt formula for potentials that vanish at infinity under minimal hypotheses, and also for general potentials under blanket geometric ergodicity assumptions. We also present associated results having the flavor of a refined maximum principle.

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Ari Arapostathis, Anup Biswas. 2018-10-02. A variational formula for risk-sensitive control of diffusions in $\mathbb{R}^d$. https://doi.org/10.1137/18m1218704

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