We study the convergence of triangular mappings on R^n, i.e., mappings T such that the ith coordinate function Ti depends only on the variables x1, . . . ,xi. We show that, under broad assumptions, the inverse mapping to ...
We consider a regression of y on x given by a pair of mean and variance functions with a parameter vector θ to be estimated that also appears in the distribution of the regressor variable x. The estimation of θ is based ...
In the article, we consider terms of the Gaussian chaotic expansion under conditioning with respect to some sigma-field and discuss the possibility to organize the orthogonal expansion from them.
Nonlinear regression model with continuous time and weak dependent or long-range dependent stationary noise is considered. Strong consistency suffient conditions of M-estimates of regression parameters are obtained.
A survey on functional limit theorems for compositions of stochastic processes is presented. Applications to stochastic processes with random scaling of time, random sums, extremes with random sample size, generalised ...
A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process controlling the price component. American ...
We obtain conditions which guarantee the existence of a decomposition of a solution of the quasilinear stochastic parabolic equation with a weak source.
Diffusion approximation algorithms for stochastic systems in split and merging phase space are represented in servey form. The main mathematical tools of such algorithms are described in our book ”Stochastic Systems in ...
Let D = [0, 1]^2 and X(s, t), (s, t) belongs D, be a two-parameter Chentsov random field. The aim of this paper is to find the probability distribution of the maximum of X(s, t) on a class of polygonal lines.
Several two-boundary problems for the Poisson process with an exponential component
are solved in the present article. The integral transforms of the joint distribution
of the epoch of the first exit from the interval and ...
We study a nonlinear measurement model where the response variable has a density belonging to the exponential family. We consider two consistent estimators: Corrected Score (CS) and Quasi Score (QS) ones. Their relative ...
We give a short historical survey on why and how the Encyclopedia has emerged. We consider both the editorial and the managerial side of the project. We indicate some of the special features of the work.
An implicit linear multivariate model DZ ≈ 0 is considered, where the data matrix D is observed with errors, and Z is a parameter matrix. The error matrix is partitioned into two uncorrelated blocks, and the total covariance ...
The theorem on a estimation of the rate of convergence (n →∞) to the Poisson distribution of the number of false solutions of a beforehand consistent system of nonlinear random equations, that has a linear part, over the ...
Using the Wiener-Hopf method, for the model with arithmetic distributions of waiting times Ti and claims Zi in ordinary renewal process, an exact non-ruin probabilities for an insurance company in terms of the factorization ...
Using the Wiener-Hopf method, for the fundamental equation of the risk theory it is obtained an exact solution in terms of the Fourier transforms and factorization.
A family of one-dimensional diffusion processes is constructed such that each one of
this family is a weak solution to some stochastic differential equation. It turns out
that the property of weak uniqueness of a solution ...
The existence and uniqueness of solution of stochastic differential equation driven by standard Brownian motion and fractional Brownian motion with Hurst parameter H belongs (3/4, 1) is established.
We consider a Gaussian centered random field that has values in the Euclidean space.
We investigate the existence of local time for the random field as a generalized functional, an element of the Sobolev space constructed ...
Integral transforms of the joint distribution of the first exit time from an interval,
the value of the overshoot through a boundary, and the value of a linear component
at the epoch of the exit are determined for the ...