càdlàg process

A càdlàg process X is a stochastic processMathworldPlanetmath for which the paths tXt are right-continuous with left limits everywhere, with probability one. The word càdlàg is an acronym from the French for “continu à droite, limites à gauche”. Such processes are widely used in the theory of noncontinuous stochastic processes. For example, semimartingales are càdlàg, and continuous-time martingalesMathworldPlanetmath and many types of Markov processes have càdlàg modifications.

Given a càdlàg process Xt with time index t ranging over the nonnegative real numbers, its left limits are often denoted by


for every t>0. Also, the jump at time t is written as


Alternative terms used to refer to a càdlàg process are rcll (right-continuous with left limits), R-process and right-process.

Although used less frequently, a process whose paths are almost surely left-continuous with right limits everywhere are known as càglàd, lcrl or L-processes.

Title càdlàg process
Canonical name CadlagProcess
Date of creation 2013-03-22 18:36:36
Last modified on 2013-03-22 18:36:36
Owner gel (22282)
Last modified by gel (22282)
Numerical id 7
Author gel (22282)
Entry type Definition
Classification msc 60G07
Synonym cadlag process
Synonym rcll process
Synonym R-process
Synonym right-process
Related topic UcpConvergenceOfProcesses
Defines cadlag
Defines rcll
Defines R-process
Defines right-process
Defines càglàd
Defines lcrl
Defines L-process