Question

Give your own example of a stochastic process that is discrete state space and discrete time. Explain why this process fits this category.

Answer 1

A stochastic process is defined as an index collection of random variables .

Where the intdex . In most real life situations this set represents time either discrete or continuous.

The set of all values taken by these random variables is known as state space of a stochastic process denoted by S can also be discrete or continuous.

An example of discrete state space and discrete time stochastic process is given below.

Consider a simple experiment of tossing a coin repeatedly and suppose is a random variable associated with n-th trial, it is 1 if head occures and 0 if tail occures. Then the set { } constitutes a stochastic process with state space {0,1} and time space {1,2,....}. Here both state space and time space are discrete.