# Stochastic Processes

Chapter

## Abstract

We commence along the lines of the founding work of Kolmogorov by regarding stochastic processes as a family of random variables defined on a probability space and thereby define a probability law on the set of trajectories of the process. More specifically, stochastic processes generalize the notion of (finite-dimensional) vectors of random variables to the case of any family of random variables indexed in a general set *T*. Typically, the latter represents “time” and is an interval of ℝ (in the continuous case) or ℕ (in the discrete case).

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© Birkhäuser Boston 2005