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Key words: Curvilinear integrals, H¨older continuity, rough paths, stochastic integrals, stochastic differential equations, fractional Brownian motion.. AMS 2000 Subject
We end this introduction by resuming the fact that results in this paper light up some explicit examples of conditioned stochastic differential equation locally equivalent to a
We give a new representation of fractional Brownian motion with Hurst parameter H ≤ 1 2 using stochastic partial differential equations.. This representation allows us to use the
Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correction term that is an ordinary Itô integral with respect to a Brownian
Abstract: In this paper we give a solution for the one-dimensional reflected backward stochastic differential equation when the noise is driven by a Brownian motion and an
Keywords Wiener space, Sobolev space, Stochastic integral, Fractional Brownian Motion, Itˆ o’s formula.. AMS Subject Classification (1991)
To prove those results, we use the fact that the ISE has the same distribution (up to a constant scaling) as the total mass of an excursion of the Brownian snake conditioned to have
This result has consequences for the Hausdorff dimension of the frontier of planar Brownian motion, and also for the Hausdorff dimension of the set of cut-points of planar
