1 Introduction

2 Probability theory; a recap

2.1 Probability

2.1.1 σ�algebra

2.1.2 Kolmogorov's axioms

2.2 Random variable

2.3 Joint distribution, marginal distribution

2.4 Transformations of a random variable

2.5 Characteristic function

2.6 Multidimensional normal distribution, non-singular and singular case

2.7 Conditional probability and conditional distribution

3 Stochastic processes

3.1 Basic properties

3.2 Poisson process

3.3 Stationarity

4 Processes in discrete time

4.1 Markov chains

4.1.1 Chapman-Kolmogorov equations

4.1.2 Classi�cation of the states

4.1.3 Stationary distribution

4.1.4 MCMC method

4.1.5 Hidden Markov chains

4.2 Time series

4.2.1 ARMA models

4.2.2 Causality, invertibility

4.2.3 Estimation of the coe�cients of ARMA models

4.2.4 Forecasting with ARMA models

5 Processes in continuous time

5.1 Wiener process

5.2 Analysis in quadratic mean

5.2.1 Continuity

5.2.2 Di�erentiability

5.2.3 Integrability

5.3 Processes with orthogonal increments

6 Spectral theory of stochastic processes

6.1 Cumulative distribution function of the spectrum

6.2 Spectral process

6.3 Processes in discrete time

6.4 Spectrum estimation

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