Geodesic
Subordinated Markov Branching Processes and Lévy Processes
Serdica Mathematical Journal, Tome 40 (2014) no. 3-4, pp. 183-208

Voir la notice de l'article provenant de la source Bulgarian Digital Mathematics Library

We consider the jump structure of the subordinated Lévy processes and subordinated Markov branching processes. Subordination provides a method of constructing a large subclass of Markov or Lévy processes Y (t) = X(T (t)), where X(t) is a Markov or Lévy process and T (t) is a continuous time subordinator independent of X(t); that is a Lévy process with positive increments and T (0) = 0. Let X(t) be a Lévy process. Then subordination preserves the independence and stationarity of the increments, but it changes their amplitudes and the total mass of the Lévy measure. Let X(t) be a Markov branching process. Then subordination (owing to the independence of X(t) and T (t)) preserves the Markov property, but it disturbs the branching property. The infinitesimal generator of the subordinated process Y (t) involves the total progeny of reproduction. The intensity of the jump times depends on the subordinator’s Bernstein function. 2010 Mathematics Subject Classification: 60J80, 60K05.
Keywords: subordinated Lévy processes, Poisson random measure, pure jump Markov processes, Kolmogorov backward equation 
@article{SMJ2_2014_40_3-4_a0,
     author = {Mayster, Penka},
     title = {Subordinated {Markov} {Branching} {Processes} and {L\'evy} {Processes}},
     journal = {Serdica Mathematical Journal},
     pages = {183--208},
     publisher = {mathdoc},
     volume = {40},
     number = {3-4},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2014_40_3-4_a0/}
}
TY  - JOUR
AU  - Mayster, Penka
TI  - Subordinated Markov Branching Processes and Lévy Processes
JO  - Serdica Mathematical Journal
PY  - 2014
SP  - 183
EP  - 208
VL  - 40
IS  - 3-4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SMJ2_2014_40_3-4_a0/
LA  - en
ID  - SMJ2_2014_40_3-4_a0
ER  - 
%0 Journal Article
%A Mayster, Penka
%T Subordinated Markov Branching Processes and Lévy Processes
%J Serdica Mathematical Journal
%D 2014
%P 183-208
%V 40
%N 3-4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SMJ2_2014_40_3-4_a0/
%G en
%F SMJ2_2014_40_3-4_a0
Mayster, Penka. Subordinated Markov Branching Processes and Lévy Processes. Serdica Mathematical Journal, Tome 40 (2014) no. 3-4, pp. 183-208. http://geodesic.mathdoc.fr/item/SMJ2_2014_40_3-4_a0/