Author | Dacunha-Castelle, Didier. author |
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Title | Probability and Statistics [electronic resource] : Volume II / by Didier Dacunha-Castelle, Marie Duflo |
Imprint | New York, NY : Springer New York, 1986 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-4870-5 |
Descript | XIV, 410 p. online resource |
0 Introduction to Random Processes -- 0.1. Random Evolution Through Time -- 0.2. Basic Measure Theory -- 0.3. Convergence in Distribution -- 1 Time Series -- 1.1. Second Order Processes -- 1.2. Spatial Processes with Orthogonal Increments -- 1.3. Stationary Second Order Processes -- 1.4. Time Series Statistics -- 2 Martingales in Discrete Time -- 2.1. Some Examples -- 2.2. Martingales -- 2.3. Stopping -- 2.4. Convergence of a Submartingale -- 2.5. Likelihoods -- 2.6. Square Intergrable Martingales -- 2.7. Almost Sure Asymptotic Properties -- 2.8. Central Limit Theorems -- 3 Asymptotic Statistics -- 3.1. Models Dominated at Each Instant -- 3.2. Contrasts -- 3.3. Rate of Convergence of an Estimator -- 3.4. Asymptotic Properties of Tests -- 4 Markov Chains -- 4.1. Introduction and First Tools -- 4.2. Recurrent or Transient States -- 4.3. The Study of a Markov Chain Having a Recurrent State -- 4.4. Statistics of Markov Chains -- 5 Step by Step Decisions -- 5.1. Optimal Stopping -- 5.2. Control of Markov Chains -- 5.3. Sequential Statistics -- 5.4. Large Deviations and Likelihood Tests -- 6 Counting Processes -- 6.1. Renewal Processes and Random Walks -- 6.2. Counting Processes -- 6.3. Poisson Processes -- 6.4. Statistics of Counting Processes -- 7 Processes in Continuous Time -- 7.1. Stopping Times -- 7.2. Martingales in Continuous Time -- 7.3. Processes with Continuous Trajectories -- 7.4. Functional Central Limit Theorems -- 8 Stochastic Integrals -- 8.1. Stochastic Integral with Respect to a Square Integrable Martingale -- 8.2. Itoโs Formula and Stochastic Calculus -- 8.3. Asymptotic Study of Point Processes -- 8.4. Brownian Motion -- 8.5. Regression and Diffusions -- Notations and Conventions