A Schilder Type Theorem for Super-Brownian Motion

Fleischmann, Klaus ; Gärtner, Jürgen ; Kaj, Ingemar

Canadian journal of mathematics, Tome 48 (1996) no. 3, pp. 542-568

Résumé

Let X be a d-dimensional continuous super-Brownian motion with branching rate ε, which might be described symbolically by the "stochastic equation" a space-time white noise. A Schilder type theorem is established concerning large deviation probabilities of X on path space as ε → 0, with a representation of the rate functional via an L 2 -functional on a generalized "Cameron-Martin space" of measure-valued paths.

Détail

DOI : 10.4153/CJM-1996-028-2

Mots-clés : 60J80, 60F10, 60G57, Schilder's Theorem, super-Brownian motion, superprocess, large deviations, rate functional, Cameron-Martin space, cumulant equation, complete blow-up

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