ON THE STRUCTURE OF SOLUTIONS OF ERGODIC TYPE BELLMAN EQUATION RELATED TO RISK-SENSITIVE CONTROL
By H. Kaise, Shuenn-Jyi Sheu. 2006
69 citations recorded by the source corpus.
Bellman equations of ergodic type related to risk-sensitive control are considered. We treat the case that the nonlinear term is positive quadratic form on first-order partial derivatives of solution, which includes linear exponential quadratic Gaussian control problem. In this paper we prove that the equation in general has multiple solutions. We shall specify the set of all the classical solutions and classify the solutions by a global behavior of the diffusion process associated with the given solution. The solution associated with ergodic diffusion process plays particular role. We shall also prove the uniqueness of such solution. Furthermore, the solution which gives us ergodicity is stable under perturbation of coefficients. Finally, we have a representation result for the solution corresponding to the ergodic diffusion.
Subfields: Control and Systems Engineering, Finance, Modeling and Simulation
View Paper: https://www.semanticscholar.org/paper/8d206a0de564ebf0c19dd248c764ec8f91beff61
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In Control and Systems Engineering
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Citations in the corpus
- Large deviations for multiscale diffusion via weak convergence methods (2010, methodology): “However, using results on the structure of solutions to ergodic type Bellman equations in Rd analogous to [26, 10] and techniques similar to the ones developed in the current paper, it is seems possible that one can prove a result that is analogous to Theorem 2.”
- Large Deviations and Importance Sampling for Systems of Slow-Fast Motion (2012, methodology): “ problem (4.14) takes the form γ 2 ξ′′ γ(y) +[γ(m−y)−σ(y)ρp]ξ′ γ(y) − 1 2 ξ′ γ(y) 2 − 1 2 σ2(y)p2 = H¯ (p) There is a unique pair (ξγ(y),H¯γ(p)) satisfying this equation such that ξγ(y) ∈ W1 loc, see [2, 26]. Notice that for this model, the solution (ξγ(y),H¯γ(p)) to the cell problem is independent ”