Stochastic Process â Definition

Before saying anything about stochastic process, we need to recall what deterministic system (or deterministic process) is?

**Deterministic System**

A system in which the later states of the system determined by the earlier states is called deterministic system.

For example, if a company defaults or face heavy loss, it is determined that the shareholders (who owns the company) will also have to face the loss.

**Stochastic Process**

The stochastic process (also called random process) is not wholly determined by the earlier one stage, but, in this case, we take observations of many random values over a period of time. So, stochastic process is a collection of random variables. And, it is a probabilistic process.

For example, we are interested in stock price of a particular company. And, we observe the stock prices at different time periods.

*S*(0) is the stock price at time = 0. *S*(1) is the stock prices at time = 1, and so on. These stock prices can take any value, so , are random variables. And, that the stock prices can move up or down, so they are independent.

**Definition of Stochastic Process**

Let *N*(*t*_{1}) be a random value when *t*=1, and *N*(*t*_{2}) be another random value when *t*=2, and so on.. And, when we consider *N*(*t*) for *tâ*[0,*â*] collectively. We say *N*(*t*) is a stochastic process or random process.

One of the most widely used stochastic process is Poisson Process.