Definition of Bernoulli Process

A process with finite or infinite sequence of independent random variables X1, X2, X3,…,satisfying the given conditions is known as Bernoulli Process:
For each i, Xi is either 0 or 1;
For all values of i, the probability that Xi = 1 is the same number p (expressed as success).
Or, we can say that a sequence of independent identically distributed bernoulli trials is known as “Bernoulli process”.
What is meant by independence of trials?
By independence of trials, it is meant that the process lacks memory which thereby implies that when the probability of success ‘p’ is known, the future outcomes are not influenced by the past outcomes or the past outcomes provide more information considering future outcomes.
(but, when p is unknown the past results tells about the future indirectly, through inferences about p.)
When the process is infinite, then from any point the future trials can constitute a Bernoulli process which is easily identical to the whole process,due to lack of memory or the fresh-start property.