Stochastic Optimal Control of First Firing Neuron

摘要

First-firing statistics of stochastic optimally controlled integrate-and-fire neuron under stimulation of colored noise is investigated. The stochastic averaging principle is utilized and the model equation is approximated by diffusion process and represented by It. stochastic differential equation. The control problems for maximizing the resting probability and maximizing mean first firing time are constructed and the dynamical programming equations associated with the corresponding optimization problem are established. The optimal control law is obtained and the finally controlled It. stochastic differential equation is yielded. The corresponding backward Kolmogorov equation and Pontryagin equation are established and solved to yield the resting probability and mean first firing time. The analytical results are verified by Monte Carlo simulation.