The notion of a dilatation structure stemmed out from my efforts to understand basic results in sub-Riemannian geometry, especially the last section of the paper by Belläıche [2] and the intrinsic point of view of Gromov [5]. In these papers, as in other articles devoted to sub-Riemannian geometry, fundamental results admiting an intrinsic formulation were proved using differential geometry too...

Let ~ and m be excessive measures for a right Markov process X and let Q~ and Qm be the associated stationary Kuznetsov processes. We show that if ~ and m are harmonic, then Q~ ~ Qm if and only if ~ is quasi-bounded by m in the sense that ~ = where each term in the sum is an excessive measure dominated by m. This result allows us to describe the Lebesgue decomposition of Q~ relative to Qm and t...

this is true for indicator functions, since ∫ 1Adπ = π(A) = ∫ A hπ,μdμ by definition of the Radon-Nikodym derivative. Then by linearity of the integral, the claim is also true for simple functions. Then we can show the claim for non-negative measurable functions, by approximating by simple functions. Indeed, if f ≥ 0 is measurable, then there exists a sequence of simple functions 0 ≤ sn ↑ f suc...

1 Summary The Radon-Nikodym derivative between a centered fractional Brownian motion Z and the same process with constant drift is derived by nding an integral transformation which changes Z to a process with independent increments. A representation of Z through a standard Brownian motion on a nite interval is given. The maximum likelihood estimator of the drift and some other applications are ...