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Tool wear will reduce workpieces' quality and accuracy. In this paper, the vibration signals of the milling process were analyzed, and it was found that historical fluctuations still have an impact on the existing state. First of all, the linear fractional alpha-stable motion (LFSM) was investigated, along with a differential iterative model with it as the noise term is constructed according to the fractional-order Ito formula; the general solution of this model is derived by semimartingale approximation. After that, for the chaotic features of the vibration signal, the time-frequency domain characteristics were extracted using principal component analysis (PCA), and the relationship between the variation of the generalized Hurst exponent and tool wear was established using multifractal detrended fluctuation analysis (MDFA). Then, the maximum prediction length was obtained by the maximum Lyapunov exponent (MLE), which allows for analysis of the vibration signal. Finally, tool condition diagnosis was carried out by the evolving connectionist system (ECoS). The results show that the LFSM iterative model with semimartingale approximation combined with PCA and MDFA are effective for the prediction of vibration trends and tool condition. Further, the monitoring of tool condition using ECoS is also effective. [ABSTRACT FROM AUTHOR]

In the same context as in the seminal paper [P. Cheridito, Bernoulli, 7 (2001), pp. 913-934], we are concerned with the semimartingale property of the sum of some Gaussian martingale and an independent fractional Brownian motion with Hurst parameter H = (0, 1). At the same time, we emphasize that the Markov property is lost even if the martingale owns it. [ABSTRACT FROM AUTHOR]

We study the existence, uniqueness and approximation of solutions of general stochastic differential equations (SDEs) with two time-dependent reflecting barriers driven by semimartingales and processes with bounded p -variation, p ∈ [ 1 , 2). We do not assume that the barriers have to be completely separated. Applications to currency option pricing in financial models with fractional Brownian motion and standard Brownian motion are given. [ABSTRACT FROM AUTHOR]

Risk measure is a fundamental concept in finance and in the insurance industry. It is used to adjust life insurance rates. In this article, we will study dynamic risk measures by means of backward stochastic Volterra integral equations (BSVIEs) with jumps. We prove a comparison theorem for such a type of equations. Since the solution of a BSVIEs is not a semimartingale in general, we will discuss some particular semimartingale issues. [ABSTRACT FROM AUTHOR]

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]

We prove that a sequence of diffusion processes in ℝ n that are Brownian motions with drift unboundedly increasing in modulus and directed to a manifold converges in distribution to the Brownian motion on the manifold. [ABSTRACT FROM AUTHOR]