A sample path large deviation principle for L2-Martingale measure processes

Boualem Djehiche, Ingemar Kaj

Research output: Contribution to journalArticlepeer-review

Abstract

Gaussian White Noise, super-brownian motion and the diffusion-limit Fleming-Viot process are examples of such infinite-dimensional Markov processes with continuous paths and L2-martingale measures we study in this work as regards to their sample path large deviation probabilities and their associated large deviation rate functions in the limit of small perturbations. We present a unified approach based on Girsanov transform techniques. We derive the rate function as a Lagrangian functional and, as an alternative representation, via some generalized derivatives in a 'Cameron-Martin space'.

Original languageEnglish (US)
Pages (from-to)467-499
Number of pages33
JournalBulletin des Sciences Mathematiques
Volume123
Issue number6
DOIs
StatePublished - Oct 1999

Keywords

  • Cameron-Martin space
  • Hamiltonian
  • Martingale measure
  • Rate function
  • Superprocess

ASJC Scopus subject areas

  • General Mathematics

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