Approximations of the brownian rough path with applications to stochastic analysis
Convergence rates for the full gaussian rough paths
Under the key assumption of finite -variation, , of the covariance of the underlying Gaussian process, sharp a.s. convergence rates for approximations of Gaussian rough paths are established. When applied to Brownian resp. fractional Brownian motion (fBM), resp. , we recover and extend the respective results of ( (2009) 2689–2718) and ( (2012) 518–550). In particular, we establish an a.s. rate , any , for Wong–Zakai and Milstein-type approximations with mesh-size...
Differential equations driven by gaussian signals
We consider multi-dimensional gaussian processes and give a new condition on the covariance, simple and sharp, for the existence of Lévy area(s). gaussian rough paths are constructed with a variety of weak and strong approximation results. Together with a new RKHS embedding, we obtain a powerful – yet conceptually simple – framework in which to analyze differential equations driven by gaussian signals in the rough paths sense.
Large deviation principle for enhanced gaussian processes
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