Oblique derivative problems and invariant measures
Occupation times of branching systems with initial inhomogeneous Poisson states and related superprocesses.
Occupation times of Lévy processes as quadratic variations
On a certain class of nonstationary sequences in Hilbert space.
On a characteristic property of the asymptotic rate
On a characterization of orthogonality with respect to particular sequences of random variables in
This note deals with the orthogonality between sequences of random variables. The main idea of the note is to apply the results on equidistant systems of points in a Hilbert space to the case of the space of real square integrable random variables. The main result gives a necessary and sufficient condition for a particular sequence of random variables (elements of which are taken from sets of equidistant elements of ) to be orthogonal to some other sequence in . The result obtained is interesting...
On a class of discrete generation interacting particle systems.
On a class of estimators in a multivariate RCA(1) model
This work deals with a multivariate random coefficient autoregressive model (RCA) of the first order. A class of modified least-squares estimators of the parameters of the model, originally proposed by Schick for univariate first-order RCA models, is studied under more general conditions. Asymptotic behavior of such estimators is explored, and a lower bound for the asymptotic variance matrix of the estimator of the mean of random coefficient is established. Finite sample properties are demonstrated...
On a class of linear models.
This paper is concerned with classification criteria, asymptotic behaviour and stationarity of a non-Markovian model with linear transition rule, called a linear OM-chain. This problems are solved by making use of the structure of the stochastic matrix appearing in the definition of such a model. The model studied includes as special cases the Markovian model as well as the linear learning model, and has applications in psychological and biological research, in control theory, and in adaptation...
On a Class of Markov Processes in Hilbert Space.
On a class of processes with multiplicity .
On a conjecture of Kazamaki
On a construction of majorizing measures on subsets of ℝⁿ with special metrics
We consider processes Xₜ with values in and “time” index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand’s majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.
On a detection method for known finite sequences
On a formula of Pollaczek and Spitzer
On a gambler's ruin problem
On a generalization of a theorem of W. Sudderth and some applications
On a Generalization of the Cauchy Equation.
On a generalization of the martingale maximal theorem
On a Martingale Related to a Strictly Stationary Random Process in R1.