# independent increment

A stochastic process $\{X(t)\mid t\in T\}$ of real-valued random variables $X(t)$, where $T$ is linearly ordered, is said have independent increments if for any $a,b,c,d\in T$ such that $a, $X(a)-X(b)$ and $X(c)-X(d)$ are independent random variables.

Remark. In case when $X(t)$ is monotonically non-decreasing, as in the case of a counting process, it is customary to write $X(b)-X(a)$ and $X(d)-X(c)$ instead of the above to emphasize the comparison of two positive quantities (for example, the numbers of occurrences of a certain event in some time intervals).

Title independent increment IndependentIncrement 2013-03-22 15:01:22 2013-03-22 15:01:22 CWoo (3771) CWoo (3771) 4 CWoo (3771) Definition msc 60G51