Abstract
The large deviation principle for stochastic line integrals along Brownian paths on a compact Riemannian manifold is studied. We regard them as a random map on a Sobolev space of 1-forms. We show that the differentiability order of the Sobolev space can be chosen to be almost independent of the dimension of the underlying space by assigning higher integrability on 1-forms. The large deviation is formulated for the joint distribution of stochastic line integrals and the empirical distribution of a Brownian path. As the result, the rate function is given explicitly.
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Kusuoka, S., Kuwada, K. & Tamura, Y. Large deviation for stochastic line integrals as L p-currents. Probab. Theory Relat. Fields 147, 649–674 (2010). https://doi.org/10.1007/s00440-009-0219-5
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DOI: https://doi.org/10.1007/s00440-009-0219-5
Keywords
- Large deviation
- Stochastic line integral
- Empirical distribution
- Current-valued process
Mathematics Subject Classification (2000)
- 60F10
- 60B12