Kolmogorov Equations Driven by Cylindrical Stable Processes and Applications to Stochastic Optimal Control

柱型穩定過程所導出之半線性Kolmogorov方程式及其在隨機最佳化控制的應用

蘇國樑(Kuo-Liang Su)

《中國統計學報》 52卷3期 (2014/09) Pp. 335-362

摘要

本文解出柱型α-穩定過程所導出之半線性Kolmogorov方程式在無限維Hilbert空間上的溫和解；其次，解出最佳化控制問題所相關之Hamilton-Jacobi-Bellman方程式的解；然後，說明在隨機控制熱傳導方程式和波動方程式上的最佳化應用。

關鍵字

Kolmogorov方程式 ； 隨機最佳化控制 ； 柱型α-穩定過程 ； Hamilton-Jacobi-Bellman方程式

並列摘要

A mild solution of semilinear Kolmogorov equations driven by a cylindrical α-stable noise is solved in an infinite dimensional Hilbert space. The associated Hamilton-Jacobi-Bellman equation is also studied and solved for applications to the stochastic optimal control problems. It then shows applications to the controlled stochastic heat equation and wave equation.

並列關鍵字

kolmogorov equation ； stochastic optimal control ； cylindrical α-stable process ； hamilton-jacobi-bellman equation

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