Lévy distance
In stochastics, the Lévy distance , also called the Lévy metric , is a measure of the correspondence between two distribution functions . It is named after Paul Lévy and is a special case of the Prokhorov metric .
definition
Denote the set of all distribution functions (in terms of stochastics) . For two one defines
- .
properties
- is a separable , complete metric space .
- The sequence of distribution functions converges weakly to a distribution function if and only if is. Thus metrisiert the Lévy metric the weak convergence of distribution functions.
Web links
- VM Zolotarev: Lévy metric . In: Michiel Hazewinkel (Ed.): Encyclopaedia of Mathematics . Springer-Verlag , Berlin 2002, ISBN 978-1-55608-010-4 (English, online ).
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 .