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.
|Date of creation||2013-03-22 18:36:36|
|Last modified on||2013-03-22 18:36:36|
|Last modified by||gel (22282)|