Càdlàg function
A Càdlàg function (also Cadlag ) is a special real-valued function that is used in stochastics , for example . Càdlàg is a French acronym (in French, continue à droite, limite à gauche, " steady on the right , with limit values from the left"). There is also the RCLL ( right continuous, left limits ) derived from the English . Analogously one speaks of Càglàd functions (or Làdcàg functions ) ( continue à gauche, limite à droite ).
definition
![](https://upload.wikimedia.org/wikipedia/commons/thumb/8/82/Discrete_probability_distribution_illustration.png/220px-Discrete_probability_distribution_illustration.png)
Be a Polish room such as . One function
called
- Càdlàg function, if for all the function in is continuous on the right and the limit on the left in exists and is finite.
- Càglàd function, if for all the function in is continuous on the left and the limit on the right in exists and is finite.
The space of all Càdlàg functions on an interval is often referred to as.
Applications in stochastics
The distribution function of a real random variable is always a Càdlàg function.
A stochastic process is called càdlàg when almost certainly every path is constant on the right at every point and the limit values on the left exist there. Poisson processes are an example of this .
literature
- Achim Klenke: Probability Theory . 3. Edition. Springer-Verlag, Berlin / Heidelberg 2013, ISBN 978-3-642-36017-6 , doi : 10.1007 / 978-3-642-36018-3 .
Web links
- Eric W. Weisstein : Cadlag Function . In: MathWorld (English).