In this paper we study the relationship between three compactifications of moduli space Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over projective algebraic manifold arbitrary dimension. Via Donaldson-Uhlenbeck-Yau theorem, is analytically isomorphic to stable holomorphic bundles, and as such it admits an compactification by Gieseker-Maruyama semistable torsion-free she...

DEVIATION INEQUALITIES AND MODERATE DEVIATIONS FOR ESTIMATORS OF PARAMETERS IN AN ORNSTEIN-UHLENBECK PROCESS WITH LINEAR DRIFT FUQING GAO School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P.R.China email: [email protected] HUI JIANG School of Science, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, P.R.China email: [email protected] Submitted December 2...

This paper establishes Fokker–Planck–Kolmogorov type equations for time-changed Gaussian processes. Examples include those equations for a time-changed fractional Brownian motion with time-dependent Hurst parameter and for a time-changed Ornstein–Uhlenbeck process. The timechange process considered is the inverse of either a stable subordinator or a mixture of independent stable subordinators.

In this paper, we adopt a Bayesian point of view for predicting real stochastic processes. We give two equivalent definition of a Bayesian predictor and study some properties: admissibility, prediction sufficiency, unbiasedness, comparison with efficient predictors. Prediction of Poisson process and prediction of Ornstein-Uhlenbeck process in the continuous and sampled situations are considered...

Moment conditions for multivariate generalized Ornstein-Uhlenbeck (MGOU) processes are derived and first and second moment are given in terms of the driving Lévy processes. In the second part of the paper a class of multivariate, positive semidefinite processes of MGOU–type is developed and suggested for use as squared volatility process in multivariate financial modelling.