Modeling and computation of an integral operator Riccati equation for an infinite-dimensional stochastic differential equation governing streamflow discharge

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is superposition Ornstein-Uhlenbeck processes (supOU process), generating sub-exponential autocorrelation function observed in actual data. The integral operator Riccati heuristically derived to determine the optimal system. In addition, its finite-dimensional version with discretized distribution reversion speed and computed finite difference scheme. optimality analyzed verification argument. supOU process parameterized based on data perennial river. convergence numerical scheme through computational experiments. Finally, we demonstrate application proposed model realistic problems along Kolmogorov backward for performance evaluation controls.