Types of Stochastic Processes

Topics: Stochastic Process

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Stochastic processes can be classified:

• According to the structure of their sets (state set $S$ and parameter set $T$).
• According to the probabilistic features of the random variable.

According to the Structure of their Sets §

$S$ / $T$	Discrete	Continuous
Discrete	Chain	Point process
Continuous	Sequence of random variables	Continuous process

According to the Probabilistic Features of the Random Variable $X_t$ §

If a stochastic process has a discrete parameter set and consists of independent random variables, then we have an independent trial process.

When a stochastic process satisfies the Markov property, we have a Markov process

When we have a stochastic process whose increments within any two random variables are independent, we have a process with independent increments.

If the probability distribution of the vector of random variables is the same for any value of $t$, then we have a stationary process.