A stochastic process is a collection of random variables. Stochastic processes play an important role in mathematical finance as they are used to model the stock prices. In this chapter, we shall present some general concepts and results about stochastic processes.

**Definition 21.1** (Stochastic Process). Let *I* be a set and (*E*, ) a measurable space. A stochastic process indexed by *I* is a family of measurable functions *X*_{t}, *t* *I*, from a probability space (Ω, , *P*) into (*E*, ). The measurable space (*E*, ) is referred to as the *state space.*

For each ω Ω, the mapping *t* → *X*_{t}(ω) is called a *trajectory* or a *sample path* of *X*.

**Definition 21.2** (Probability Law of Stochastic Process). Let {*X*_{t} : *t* *I*} be a stochastic process on some probability space ...

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