Approximation of some classes of random processes by cubic splines with given accuracy and reliability is considered. Estimations of deviation of approximating spline from original process are obtained. A few examples of ...
Asymptotic formulas for large-deviation probabilities of a ladder height in a random
walk generated by a sequence of sums of i.i.d. random variables are deduced.
Two cases are considered:
a) the distribution F(x) of ...
Some sufficient conditions for consistency and asymptotic normality of a non-linear regression parameter Lp-estimator are presented for a continuous time regression model with Gaussian stationary noise possessing the ...
Using the method of the classical potential theory, we have constructed a semigroup of operators that describes a multidimensional process of Brownian motion, for which the drift vector and the diffusion matrix are generalized ...
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 ...
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 ...
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.
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 ...
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 ...
The nonlinear structural errors-in-variables model is investigated. We consider a Simex estimator with polynomial extrapolation function. The expansion of a Simex estimator is based on the asymptotic expansion of a naive ...
An explicit procedure to construct a family of martingales generated by a process with independent increments is presented. The main tools are the polynomials that give the relationship between the moments and cumulants, ...
The paper is devoted to the problem of quantile hedging of contingent claims in the framework of a model defined by the finite number of independent Brownian and fractional Brownian motions. The maximal success probability ...
The asymptotic behavior of the general type third order non-autonomous oscillating system under the action of small non-linear random periodic perturbations of "white" and "Poisson" types in resonance case is investigated.
We consider the symmetric Markovian random evolution X(t) performed by a particle that moves with constant finite speed c in the Euclidean space R^m, m >= 2. Its motion is subject to the control of a homogeneous Poisson ...
The (normalized) number of sign changes for a weakly convergent sequence of onedimensional diffusion processes is considered. The limit theorem for this number is established.
We prove the existence and uniqueness of strong solutions for linear stochastic differential equations in the space dual to a multi–Hilbertian space driven by a finite dimensional Brownian motion under relaxed assumptions ...