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math.PR2009
Non-Linear Evolution Equations Driven by Rough Paths
Thomas Cass, Zhongmin Qian, Jan Tudor
We prove existence and uniqueness results for (mild) solutions to some non-linear parabolic evolution equations with a rough forcing term. Our method of proof relies on a careful e…
math.PR2009
A Large Deviation Principle for Martingales over Brownian Filtration
Z. Qian, C. Xu
In this article we establish a large deviation principle for the family {ν_ε:ε\in (0,1)} of distributions of the scaled stochastic processes {P_{-\log\sqrtε}Z_t}_{t\leq 1}, where (…