## You are here

Homeindependent increment

## Primary tabs

# 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 $a<b<c<d$, $X(a)-X(b)$ 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).

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

60G51*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections