A Variational Formula for Risk-Sensitive Control of Diffusions in $\mathbb{R}^d$

DOI10.1137/18M1218704zbMath1428.35246arXiv1810.01180MaRDI QIDQ5208746

Anup Biswas, Aristotle Arapostathis

Publication date: 10 January 2020

Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.01180

zbMATH Keywords

principal eigenvalueCollatz-Wielandt formulaDonsker-Varadhan functionalmin-max formulasemilinear PDE(Agmon) ground state

Mathematics Subject Classification ID

Continuous-time Markov processes on general state spaces (60J25) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Estimates of eigenvalues in context of PDEs (35P15) Optimal stochastic control (93E20) Diffusion processes (60J60) Large deviations (60F10)

Related Items (10)

Nonzero-sum risk-sensitive stochastic differential games: a multi-parameter eigenvalue problem approach ⋮ Long-Run Risk-Sensitive Impulse Control ⋮ Risk-sensitive zero-sum stochastic differential game for jump-diffusions ⋮ A variational characterization of the optimal exit rate for controlled diffusions ⋮ Generalized principal eigenvalues of convex nonlinear elliptic operators in \(\mathbb{R}^N\) ⋮ On the policy improvement algorithm for ergodic risk-sensitive control ⋮ A Variational Characterization of the Risk-Sensitive Average Reward for Controlled Diffusions on $\mathbb{R}^d$ ⋮ “Controlled” Versions of the Collatz–Wielandt and Donsker–Varadhan Formulae ⋮ Ergodic risk-sensitive control for regime-switching diffusions ⋮ Risk-sensitive control for a class of diffusions with jumps

Cites Work

• Unnamed Item
• Risk-sensitive control and an abstract Collatz-Wielandt formula
• Risk sensitive control of diffusions with small running cost
• On general minimax theorems
• The Dirichlet problem for the Bellman equation at resonance
• On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications
• Strict monotonicity of principal eigenvalues of elliptic operators in \(\mathbb R^d\) and risk-sensitive control
• Infinite horizon risk-sensitive control of diffusions without any blanket stability assumptions
• Zero-sum stochastic differential games with risk-sensitive cost
• An eigenvalue approach to the risk sensitive control problem in near monotone case
• Principal eigenvalues and the Dirichlet problem for fully nonlinear elliptic operators
• On the principal eigenvalue of elliptic operators in \(\mathbb R^N\) and applications
• Nonlinear Perron–Frobenius Theory
• Ergodic Control of Diffusion Processes
• On a Variational Formula for the Principal Eigenvalue for Operators with Maximum Principle
• On the principal eigenvalue of second-order elliptic differential operators
• The principal eigenvalue and maximum principle for second‐order elliptic operators in general domains
• Generalizations and Properties of the Principal Eigenvalue of Elliptic Operators in Unbounded Domains
• A Variational Characterization of the Risk-Sensitive Average Reward for Controlled Diffusions on $\mathbb{R}^d$

This page was built for publication: A Variational Formula for Risk-Sensitive Control of Diffusions in $\mathbb{R}^d$