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It is shown that every adapted Brownian bridge on a geodesically complete connected Riemannian manifold is a semimartingale including its terminal time, without any further assumptions on the geometry. In particular, it follows that every such process can be horizontally lifted to a smooth principal fiber bundle with connection, including its terminal time. The proof is based on a localized Hamilton-type gradient estimate. [ABSTRACT FROM AUTHOR]

In this paper, we consider the optimal approximation of a Rosenblatt process based on semimartingales of the formwhere (y1,y2)↦a(y1,y2) is a square integrable process andBis a standard Brownian motion. We show that there exists a unique semimartingale closest to Rosenblatt process ifais deterministic. [ABSTRACT FROM PUBLISHER]

Starting from the moving average representation of fractional Brownian motion, there are two different approaches to constructing fractional Lévy processes in the literature. Applying L2-integration theory, one can keep the same moving average kernel and replace the driving Brownian motion by a pure jump Lévy process with finite second moments. Alternatively, in the framework of alpha-stable random measures, the Brownian motion is replaced by an alpha-stable Lévy process and the exponent in the kernel is reparametrized by H - \/a. We now provide a unified approach taking kernels of the form a((t - s)γ+ - (-s)γ+) + b((t - s)γ- - (-s)γ-), where γ can be chosen according to the existing moments and the Blumenthal-Getoor index of the underlying Lévy process. These processes may exhibit both long and short range dependence. In addition we will examine further properties of the processes, e.g., regularity of the sample paths and the semimartingale property. [ABSTRACT FROM AUTHOR]