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On Itô differential equation in rough path theory
Published 11 Jun 2013 in math.PR | (1306.2589v2)
Abstract: The solution of rough differential equation, driven by the It^o signature of a continuous local martingale, exists uniquely a.s. when the vector field is Lip(\beta) for \beta > 1, and coincides a.s. with the It^o signature of the solution of parallel stochastic differential equation. Moreover, the It^o solution can be recovered pathwisely by concatenating discounted Stratonovich solutions.
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