Stochastic calculus, statistical asymptotics, Taylor strings and phyla

Stochastic Taylor expansions and heat kernel asymptotics

3 Stochastic Taylor expansions 5 3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 3.2 Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Brownian Chen series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.4 Exponential of a vector field . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.5 Li...

Flows and stochastic Taylor series in Itô calculus

Statistical aspects of the fractional stochastic calculus

We apply the techniques of stochastic integration with respect to the fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift parameter of stochastic processes satisfying stochastic equations driven by fractional Brownian motion with any level of Holder-regularity (any Hurst parameter...

On the Taylor functional calculus

We give a Martinelli-Vasilescu type formula for the Taylor functional calculus and a simple proof of its basic properties.

Fractional Calculus and the Taylor-riemann Series

In this paper we give some background theory on the concept of fractional calculus, in particular the Riemann-Liouville operators. We then investigate the Taylor-Riemann series using Osler’s theorem and obtain certain double infinite series expansions of some elementary functions. In the process of this we give a proof of the convergence of an alternative form of Heaviside’s series. A Semi-Tayl...