Details

Autor(en) / Beteiligte

• Yoshioka, Hidekazu
• Tsujimura, Motoh

Titel

Derivation and Computation of Integro-Riccati Equation for Ergodic Control of Infinite-Dimensional SDE

Ist Teil von

• Computational Science – ICCS 2022, p.577-588

Ort / Verlag

Cham: Springer International Publishing

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Optimal control of infinite-dimensional stochastic differential equations (SDEs) is a challenging topic. In this contribution, we consider a new control problem of an infinite-dimensional jump-driven SDE with long (sub-exponential) memory arising in river hydrology. We deal with the case where the dynamics follow a superposition of Ornstein–Uhlenbeck processes having distributed reversion speeds (called supOU process in short) as found in real problems. Our stochastic control problem is of an ergodic type to minimize a long-run linear-quadratic objective. We show that solving the control problem reduces to finding a solution to an integro-Riccati equation and that the optimal control is infinite-dimensional as well. The integro-Riccati equation is numerically computed by discretizing the phase space of the reversion speed. We use the supOU process with an actual data of river discharge in a mountainous river environment. Computational performance of the proposed numerical scheme is examined against different discretization parameters. The convergence of the scheme is then verified with a manufactured solution. Our paper thus serves as new modeling, computation, and application of an infinite-dimensional SDE.