Large deviation principle for certain spatially lifted Gaussian rough path

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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.

Original languageEnglish
Pages (from-to)433-463
Number of pages31
JournalTohoku Mathematical Journal
Volume67
Issue number3
DOIs
Publication statusPublished - 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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