Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations

I. Stojkovic; O. van Gaans

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 4, page 1121-1146
  • ISSN: 0246-0203

Abstract

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We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.

How to cite

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Stojkovic, I., and van Gaans, O.. "Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations." Annales de l'I.H.P. Probabilités et statistiques 47.4 (2011): 1121-1146. <http://eudml.org/doc/242357>.

@article{Stojkovic2011,
abstract = {We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.},
author = {Stojkovic, I., van Gaans, O.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {Delay equation; invariant measure; Lévy process; semimartingale; Skorohod space; stability; tightness; variation-of-constants formula; delay equation},
language = {eng},
number = {4},
pages = {1121-1146},
publisher = {Gauthier-Villars},
title = {Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations},
url = {http://eudml.org/doc/242357},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Stojkovic, I.
AU - van Gaans, O.
TI - Invariant measures and a stability theorem for locally Lipschitz stochastic delay equations
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 1121
EP - 1146
AB - We consider a stochastic delay differential equation with exponentially stable drift and diffusion driven by a general Lévy process. The diffusion coefficient is assumed to be locally Lipschitz and bounded. Under a mild condition on the large jumps of the Lévy process, we show existence of an invariant measure. Main tools in our proof are a variation-of-constants formula and a stability theorem in our context, which are of independent interest.
LA - eng
KW - Delay equation; invariant measure; Lévy process; semimartingale; Skorohod space; stability; tightness; variation-of-constants formula; delay equation
UR - http://eudml.org/doc/242357
ER -

References

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