TAILIEUCHUNG - Existence of linear-quadratic regulator for degenerate diffusions

This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation. | Turk J Math 30 (2006) , 309 – 328. ¨ ITAK ˙ c TUB Existence of Linear-Quadratic Regulator for Degenerate Diffusions Azizul Baten Abstract This paper studies a linear regulatory quadratic control problem for degenerate Hamilton-Jacobi-Bellman (HJB) equation. We establish the existence of a unique viscosity and a classical solution of the degenerate HJB equation associated with this problem by the technique of viscosity solutions, and, hence, derive an optimal control from the optimality conditions in the HJB equation. Key words and phrases: Stochastic differential equation, Hamilton-Jacobi-Bellman equation, Linear-Quadratic problem, Viscosity solutions, Applications to control theory. 1. Introduction We are concerned with the quadratic control problem to minimize the expected cost with discount factor β > 0: Z J(c) = E ∞ e−βt {h(xt ) +

• Toán học
• Stochastic differential equation
• Hamilton Jacobi Bellman equation
• Linear Quadratic problem
• Viscosity solutions
• Applications to control theory
• Asymptotic stability
• Nonautonomous second order stochastic delay
• Differential equation
• Lyapunov functional
• Engineered systems
• numerical scheme for solutions of stochastic advection diffusion equations
• stochastic advection diffusion equations
• Stochastic partial differential equation
• Finite difference method
• convergence stability
• Random walk
• Itô´s lemma
• Lognormal distribution
• Itô´s stochastic differential equation
• Partial differential equation
• Integral Equation
• Transference Principle
• Stochastic Differential
• Evolution Equation
• Some Quasilinear
• Resolvent Estimates
• Derivative securities
• stochastic volatility
• stock options
• quantum mechanics
• rigid propagator
• Empirical analysis
• Tạp chí khoa học
• Khoa học tự nhiên
• Delay equation
• Almost sure exponential stability
• Ito formula
• Lyapunov function
• Fractional Brownian motion
• Non colliding particle systems
• Colliding particle systems
• Twodimensional fractional
• Fractional Bessel process
• Fractional stochastic differential equation
• Malliavin derivative
• Malliavin calculus
• Inverse moments