Editing Stochastic process (section)

===Increment===
An '''increment''' of a stochastic process is the difference between two random variables of the same stochastic process. For a stochastic process with an index set that can be interpreted as time, an increment is how much the stochastic process changes over a certain time period. For example, if <math>\{X(t):t\in T \}</math> is a stochastic process with state space <math>S</math> and index set <math>T=[0,\infty)</math>, then for any two non-negative numbers <math>t_1\in [0,\infty)</math> and <math>t_2\in [0,\infty)</math> such that <math>t_1\leq t_2</math>, the difference <math>X_{t_2}-X_{t_1}</math> is a <math>S</math>-valued random variable known as an increment.<ref name="KarlinTaylor2012page27"/><ref name="Applebaum2004page1337"/> When interested in the increments, often the state space <math>S</math> is the real line or the natural numbers, but it can be <math>n</math>-dimensional Euclidean space or more abstract spaces such as [[Banach space]]s.<ref name="Applebaum2004page1337"/>