Controlled linear stochastic systems with coefficients depending on a random sequence (Q1293603)

The author studies a controlled linear stochastic recurrent equation \[ \xi_{k+1}=a_k(\theta)\xi_k+b_k(\theta)\eta_k+g_{1k}(\theta,\xi_k)w_{1k}g_{2k} (\theta,\eta_k)w_{2k}+g_{3k}(\theta)w_{3k} \] with coefficients depending on a sequence of random elements with a known joint distribution. The random sequences \(w_1\), \(w_2\), \(w_3\) and \(\theta\) are supposed to be mutually independent. An optimal control problem with respect to a quadratic cost function is considered, and its explicit form is presented in terms of the coefficients of the equation and some conditional matrices. The case when \(\theta_0,\dots,\theta_{N-1}\) create a Markov chain is considered as a particular one.