Smoothing signals for semimartingales

Smoothing Signals for Semimartingales

Some norm estimates for semimartingales

In this paper we introduce a new type of norm for semimartingales. Our norm is defined in the spirit of quasimartingales, and it characterizes square integrable semimartingales. This work is motivated by our study of zero-sum stochastic differential games, whose value process we conjecture to be a semimartingale under a class of probability measures under some conditions. The norm introduced he...

Optimal Nonparametric Estimation for Semimartingales

This paper extends a result of Godambe on parametric estimation for discrete time stochastic processes to nonparametric estimation for the continuous time case. Following Hasminskii and Ibragimov (1980), the nonparametric problem is formulated as a parametric one but with infinite dimensional parameter. Let { P } be a family of probability measures such that (D,F,P) is complete , (Ft,t~O) is a ...

Smoothing of discontinuous signals: the competitive approach

Discontinuous signals buried in noise cannot be recovered by linear filtering methods. This paper presents a new class of nonlinear filters in which sets of forward and backward linear predictors and smoothers compete with each other at each timestep. The winner of each competition is granted the right to produce the smoothed estimate at that timestep. This conceptually simple approach to nonli...

An Automatic Sequential Smoothing Method for Processing Biomechanical Kinematic Signals

The combined application of Singular Spectrum Analysis (SSA) and Cluster Analysis to the automatic smoothing of raw kinematic signals is an alternative to the use of traditional digital filtering and spline based methods. SSA is a non parametric technique that decomposes original time series into a number of additive time series each of which can be easily identified as being part of the noise ...