Journal of Theoretical Probability

, Volume 11, Issue 1, pp 1–24

Large Deviations for Hierarchical Systems of Interacting Jump Processes

  • Boualem Djehiche
  • Alexander Schied

DOI: 10.1023/A:1021690707556

Cite this article as:
Djehiche, B. & Schied, A. Journal of Theoretical Probability (1998) 11: 1. doi:10.1023/A:1021690707556


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.

Two-level hierarchical interactionMcKean–Vlasov limitlarge deviationsOrlicz spacemeasure-valued processesweak interactionepidemic process

Copyright information

© Plenum Publishing Corporation 1998

Authors and Affiliations

  • Boualem Djehiche
    • 1
  • Alexander Schied
    • 2
  1. 1.Division of Mathematical StatisticsThe Royal Institute of TechnologyStockholmSweden
  2. 2.Institut für MathematikHumboldt-UniversitätBerlinGermany