Stochastic Process Essay

564 Words2 Pages

A stochastic process, sometimes called random process, is a family (collection) of random variables which presents the evolution of some random values over the time. There are two categories of stochastic processes:
A discrete time stochastic process which is described as a sequence of random variables known as time series (Markov chain). The values of variables change at the fixed points of the time.
Continuous time stochastic processes are presented as a function whose values are random variables with certain probability distributions. The values of variables change continuously over time.
Good examples of stochastic process among many are exchange rate and stock market fluctuations, blood pressure, temperature, Brownian motion, random walk.
A Markov chain is a stochastic process where the past history of variables are irrelevant and only the present value is important for the predicting the future one.
So Markov chain property can be expressed as:

Pr⁡(X_(n+1)=x┤| X_1=x_1,X_2=x_2,…,X_n=x_n)=Pr⁡(X_(n+1)=x┤| X_n=x_n)

where X_1,X_2,X_3,… are random variables.

A Wiener process k...

More about Stochastic Process Essay

Open Document