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

✍ Scribed by Boualem Djehiche; Ingemar Kaj

• Publisher: Elsevier Science
• Year: 1999
• Tongue: French
• Weight: 196 KB
• Volume: 123
• Category: Article
• ISSN: 0007-4497
• DOI: 10.1016/s0007-4497(99)00107-4

✦ Synopsis

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 L 2 -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'.