On computing the OC and ASN for some Markovian SPRT's
On conditional independence and log-convexity
If conditional independence constraints define a family of positive distributions that is log-convex then this family turns out to be a Markov model over an undirected graph. This is proved for the distributions on products of finite sets and for the regular Gaussian ones. As a consequence, the assertion known as Brook factorization theorem, Hammersley–Clifford theorem or Gibbs–Markov equivalence is obtained.
On covariance coefficients estimates of finite order moving average processes
On covariance generating functions and spectral densities of periodically correlated autoregressive processes.
On Covariance Of Spectral Estimates Of Stationary Random Sequence
On cumulative process model and its statistical analysis
The notion of the counting process is recalled and the idea of the ‘cumulative’ process is presented. While the counting process describes the sequence of events, by the cumulative process we understand a stochastic process which cumulates random increments at random moments. It is described by an intensity of the random (counting) process of these moments and by a distribution of increments. We derive the martingale – compensator decomposition of the process and then we study the estimator of the...
On discrete Fourier analysis of amplitude and phase modulated signals
In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal , t=0,1,...,n-1, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances of such...
On discrete Fourier spectrum of a harmonic with random frequency modulation
Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., n-1 by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as n → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations with...
On estimating the diffusion coefficient
On estimating the diffusion coefficient [Abstract of thesis]
On estimating the diffusion coefficient : parametric versus nonparametric
On estimating the memory for finitarily markovian processes
On estimating the yield and volatility curves
On estimation and detection of infinite-variable functions.
On estimation in random fields generated by linear stochastic partial differential equations
On estimation of a covariance function of stationary errors in a nonlinear regression model.
On expontential autoregressive time series models.
On extrapolation in multiple ARMA processes
On Extrapolation of Moving Average and Autoregressive Processes
On filtering over Îto-Volterra observations.