Resonance phenomena for second-order stochastic control equations
Patricio Felmer, Alexander Quaas, Boyan Sirakov
TL;DR
This paper investigates the existence and characteristics of solutions to second-order stochastic control equations, focusing on how principal eigenvalues influence the solutions of elliptic Hamilton-Jacobi-Bellman operators.
Contribution
It provides new insights into the role of principal eigenvalues in the existence and properties of solutions for second-order stochastic control equations.
Findings
Existence criteria for solutions based on eigenvalues
Properties of solutions related to eigenvalue variations
Impact of eigenvalues on solution behavior
Abstract
We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-Jacobi-Bellman operators, depending on the principal eigenvalues of the operator.
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