# càdlàg process

A càdlàg process $X$ is a stochastic process^{} for which the paths $t\mapsto {X}_{t}$ 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 martingales^{} and many types of Markov processes have càdlàg modifications.

Given a càdlàg process ${X}_{t}$ 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

$$\mathrm{\Delta}{X}_{t}={X}_{t}-{X}_{t-}.$$ |

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 |