Infinite Horizon Stochastic Maximum Principle for Stochastic Delay Evolution Equations in Hilbert Spaces

2021 ◽  
Author(s):  
Haoran Dai ◽  
Jianjun Zhou ◽  
Han Li
Keyword(s):  
Maximum Principle ◽  
Hilbert Spaces ◽  
Evolution Equations ◽  
Infinite Horizon ◽  
Stochastic Maximum Principle ◽  
Stochastic Delay

scholarly journals Infinite Horizon Optimal Control of Stochastic Delay Evolution Equations in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-14
Author(s):  
Xueping Zhu ◽  
Jianjun Zhou
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Hilbert Spaces ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Infinite Horizon ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

The aim of the present paper is to study an infinite horizon optimal control problem in which the controlled state dynamics is governed by a stochastic delay evolution equation in Hilbert spaces. The existence and uniqueness of the optimal control are obtained by means of associated infinite horizon backward stochastic differential equations without assuming the Gâteaux differentiability of the drift coefficient and the diffusion coefficient. An optimal control problem of stochastic delay partial differential equations is also given as an example to illustrate our results.

scholarly journals Controllability of semilinear stochastic delay evolution equations in Hilbert spaces

2002 ◽  
Vol 31 (3) ◽  
pp. 157-166 ◽  
Author(s):  
P. Balasubramaniam ◽  
J. P. Dauer
Keyword(s):  
Fixed Point ◽  
Partial Differential Equations ◽  
Fixed Point Theorem ◽  
Hilbert Spaces ◽  
Stochastic Partial Differential Equations ◽  
Evolution Equations ◽  
Semigroup Theory ◽  
Banach Fixed Point Theorem ◽  
Stochastic Delay ◽  
Stochastic Version

The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given.

Malliavin calculus used to derive a stochastic maximum principle for system driven by fractional Brownian and standard Wiener motions with application

2020 ◽  
Vol 28 (4) ◽  
pp. 291-306
Author(s):  
Tayeb Bouaziz ◽  
Adel Chala
Keyword(s):  
Brownian Motion ◽  
Maximum Principle ◽  
Control Problem ◽  
Fractional Brownian Motion ◽  
Stochastic Control ◽  
Malliavin Calculus ◽  
Stochastic Maximum Principle ◽  
Hurst Parameter ◽  
Principle Of Optimality ◽  
Initial Cost

AbstractWe consider a stochastic control problem in the case where the set of the control domain is convex, and the system is governed by fractional Brownian motion with Hurst parameter {H\in(\frac{1}{2},1)} and standard Wiener motion. The criterion to be minimized is in the general form, with initial cost. We derive a stochastic maximum principle of optimality by using two famous approaches. The first one is the Doss–Sussmann transformation and the second one is the Malliavin derivative.

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