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Continuous Time Stochastic Processes

Part I. Continuous Time Stochastic Processes

1. Covariance Stationary Stochastic Processes
2. Mean Square Continuity and Differentiability of a Stochastic Process
3. The Poisson Counting Process
4. The Concept of “Physical Realizability”
5. Stochastic Processes Driven by a Poisson Counting Process
6. The Wiener Process
7. Stochastic Differential Equations Driven by a Wiener Process
8. Spectral Densities
9. Characterizations of Mean Square Differentiability and Mean Square Continuity
10. The Cramér Representation
11. Linear Stochastic Differential Equations
12. Linear Least Squares Prediction
13. Locally Unpredictable Stochastic Processes
14. Examples of Nonstationary Processes
15. State-Space Models, the Kalman Filter, and Spectral Factorization
16. Faster Methods for Solving Recursive Linear Models of Dynamic Economies
17. Discrete Sampling: The Folding Formula

Part II. Companion Papers: Aggregation, Prediction, Identification

18. Time Aggregation
19. Prediction Formulas for Continuous Time Linear Rational Expectations Models
20. Aggregation Over Time and the Inverse Optimal Predictor Problem for Adaptive Expectations in Continuous Time
21. Inferring a Continuous-Time System from Discrete-Time Data: An Appreciation of A. W. Phillips (1959)
22. The Dimensionality of the Aliasing Problem in Models with Rational Spectral Densities
23. Temporal Aggregation of Economic Time Series

Appendices

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By Thomas J. Sargent