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Optimal Stochastic Control

Definition

Admissible Policy

Definition

Average Infinite Horizon Optimization

Theorem

Bellman's Optimality Principle

Theorem

Blackwell's Irrelevant Information Theorem

Theorem

Controllability & Observability w.r.t. Riccati

Definition

Controlled Markov Chain

Theorem

Discounted Cost

Definition

Discounted Infinite Horizon Optimization

Definition

Finite Horizon Optimization

Theorem

Linear Quadratic Problem

Definition

Markov Decision Process

Definition

Markov Policy

Definition

Markov Policy induces Markov Chain

Theorem

Markov Policy is Good Enough

Definition

Measurable Selection Conditions

Definition

Near Optimal

Definition

Optimal

Definition

Policy

Theorem

Policy Relationships

Theorem

Riccati Equation

Definition

Stationary Policy

Theorem

Value Iteration Algorithm

Definition

ε-Optimal