Stochastic Processes

  1. Renewal Theory
    1. Renewal Processes
      1. Definition and Examples
        1. Inter-renewal Times
          1. Renewal Counting Process
            1. Sample Path Properties
            2. Renewal Function
              1. Definition and Properties
                1. Renewal Equation
                  1. Solution Methods
                    1. Asymptotic Behavior
                    2. Limit Theorems
                      1. Elementary Renewal Theorem
                        1. Statement and Proof
                          1. Rate of Renewals
                          2. Blackwell's Renewal Theorem
                            1. Statement and Conditions
                            2. Key Renewal Theorem
                              1. Statement and Applications
                                1. Directly Riemann Integrable Functions
                              2. Renewal-Reward Processes
                                1. Definition and Setup
                                  1. Reward Structure
                                    1. Long-Run Average Reward
                                      1. Renewal-Reward Theorem
                                      2. Age and Residual Life
                                        1. Current Age Process
                                          1. Residual Life Process
                                            1. Limiting Distributions
                                              1. Inspection Paradox
                                              2. Applications
                                                1. Replacement Models
                                                  1. Inventory Theory
                                                    1. Reliability Analysis
                                                    2. Generalizations
                                                      1. Alternating Renewal Processes
                                                        1. Delayed Renewal Processes
                                                          1. Stationary Renewal Processes

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                                                        7. Martingales