càdlàg process
A càdlàg process is a stochastic process for which the paths 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 with time index ranging over the nonnegative real numbers, its left limits are often denoted by
for every . Also, the jump at time 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 |