On the Problem of Minimum Asymptotic Exit Rate for Stochastically Perturbed Multi-Channel Dynamical Systems


We tend to take into account the matter of minimizing the asymptotic exit rate with that the controlled-diffusion method of a stochastically perturbed multi-channel dynamical system exits from a given bounded open domain. In specific, for a class of admissible bounded linear feedback operators, we establish a affiliation between the asymptotic exit rate with that such a controlled-diffusion method exits from the given domain and therefore the asymptotic behavior (i.e., a probabilistic characterization) of the principal eigenvalue of the infinitesimal generator, that corresponds to the stochastically perturbed dynamical system, with zero boundary conditions on the given domain. Finally, we tend to briefly remark on the implication of our result for evaluating the performance of the associated deterministic multi-channel dynamical system, when such a dynamical system consists with a group of (sub)-optimal admissible linear feedback operators.

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