Tohoku Mathematical Journal
2015
September
SECOND SERIES VOL. 67, NO. 3

Tohoku Math. J.
67 (2015), 433-463

Title LARGE DEVIATION PRINCIPLE FOR CERTAIN SPATIALLY LIFTED GAUSSIAN ROUGH PATH

Author Yuzuru Inahama

(Received February 6, 2014, revised June 16, 2014)
Abstract. In rough stochastic PDE theory of Hairer type, rough path lifts with respect to the space variable of two-parameter continuous Gaussian processes play a main role. A prominent example of such processes is the solution of the stochastic heat equation under the periodic condition. The main objective of this paper is to show that the law of the spatial lift of this process satisfies a Schilder type large deviation principle on the continuous path space over a geometric rough path space.

Mathematics Subject Classification. Primary 60F10; Secondary 60H15, 60H99.
Key words and phrases. Rough path theory, large deviation principle, stochastic partial differential equation.

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