Large Deviations for Hierarchical Systems of Interacting Jump Processes

Boualem Djehiche; Alexander Schied

doi:10.1023/A:1021690707556

Large Deviations for Hierarchical Systems of Interacting Jump Processes

Boualem Djehiche, Alexander Schied

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate the large deviations principle from the McKean-Vlasov limit for a collection of jump processes obeying a two-level hierarchy interaction. A large deviation upper bound is derived and it is shown that the associated rate function admits a Lagrangian representation as well as a nonvariational one. Moreover, it is proved that the admissible paths for the weak solution of the McKean-Vlasov equation enjoy certain strong differentiability properties.

Original language	English (US)
Pages (from-to)	1-24
Number of pages	24
Journal	Journal of Theoretical Probability
Volume	11
Issue number	1
DOIs	https://doi.org/10.1023/A:1021690707556
State	Published - 1998

Keywords

Epidemic process
Large deviations
McKean-Vlasov limit
Measure-valued processes
Orlicz space
Two-level hierarchical interaction
Weak interaction

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

Access to Document

10.1023/A:1021690707556

Cite this

@article{fc336328dfff45d09b911d72aa531013,

title = "Large Deviations for Hierarchical Systems of Interacting Jump Processes",

abstract = "We investigate the large deviations principle from the McKean-Vlasov limit for a collection of jump processes obeying a two-level hierarchy interaction. A large deviation upper bound is derived and it is shown that the associated rate function admits a Lagrangian representation as well as a nonvariational one. Moreover, it is proved that the admissible paths for the weak solution of the McKean-Vlasov equation enjoy certain strong differentiability properties.",

keywords = "Epidemic process, Large deviations, McKean-Vlasov limit, Measure-valued processes, Orlicz space, Two-level hierarchical interaction, Weak interaction",

author = "Boualem Djehiche and Alexander Schied",

year = "1998",

doi = "10.1023/A:1021690707556",

language = "English (US)",

volume = "11",

pages = "1--24",

journal = "Journal of Theoretical Probability",

issn = "0894-9840",

publisher = "Springer New York",

number = "1",

}

TY - JOUR

T1 - Large Deviations for Hierarchical Systems of Interacting Jump Processes

AU - Djehiche, Boualem

AU - Schied, Alexander

PY - 1998

Y1 - 1998

N2 - We investigate the large deviations principle from the McKean-Vlasov limit for a collection of jump processes obeying a two-level hierarchy interaction. A large deviation upper bound is derived and it is shown that the associated rate function admits a Lagrangian representation as well as a nonvariational one. Moreover, it is proved that the admissible paths for the weak solution of the McKean-Vlasov equation enjoy certain strong differentiability properties.

AB - We investigate the large deviations principle from the McKean-Vlasov limit for a collection of jump processes obeying a two-level hierarchy interaction. A large deviation upper bound is derived and it is shown that the associated rate function admits a Lagrangian representation as well as a nonvariational one. Moreover, it is proved that the admissible paths for the weak solution of the McKean-Vlasov equation enjoy certain strong differentiability properties.

KW - Epidemic process

KW - Large deviations

KW - McKean-Vlasov limit

KW - Measure-valued processes

KW - Orlicz space

KW - Two-level hierarchical interaction

KW - Weak interaction

UR - http://www.scopus.com/inward/record.url?scp=0032396537&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032396537&partnerID=8YFLogxK

U2 - 10.1023/A:1021690707556

DO - 10.1023/A:1021690707556

M3 - Article

AN - SCOPUS:0032396537

SN - 0894-9840

VL - 11

SP - 1

EP - 24

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 1

ER -

Large Deviations for Hierarchical Systems of Interacting Jump Processes

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this