On some inequalities of local times of iterated stochastic integrals.
On some limit properties of the reward from a Markov replacement process
On some maximal inequalities for demisubmartingales and -demisuper martingales.
On some mean oscillation inequalities for martingales.
On some properties of J-convex stochastic processes.
On some properties of the Lüroth-type alternating series representations for real numbers.
On some regularity properties of solutions to stochastic evolution equations in Hilbert spaces
On some sample path properties of Skorohod integral processes
On spectral bandwidth of a stationary random process
The irregularity coefficient is one of the numerical characteristics of the spectral bandwith of a stationary random process. Its basic properties are investigated and the application to the dichotomic classification of a process into narrow-band and wide-band ones is given. Further, its behaviour is analyzed for sufficiently wide classes of stationary processes whose spectral densities frequently appear both in theory and applications.
On spectral type of nonanticipative transformation of Wiener process
On stationarity of a multiple doubly stochastic model
On strictly sparse subsets of a free group.
On subexponential distributions and asymptotics of the distribution of the maximum of sequential sums.
On subsets of and -stable processes
On sums of i.i.d. random variables indexed by N parameters
On sums of independent random variables without power moments.
On suprema of Lévy processes and application in risk theory
Let X̂=C−Y where Y is a general one-dimensional Lévy process and C an independent subordinator. Consider the times when a new supremum of X̂ is reached by a jump of the subordinator C. We give a necessary and sufficient condition in order for such times to be discrete. When this is the case and X̂ drifts to −∞, we decompose the absolute supremum of X̂ at these times, and derive a Pollaczek–Hinchin-type formula for the distribution function of the supremum.
On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes
We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded...
On the accuracy of approximation of the distribution of negative-binomial random sums by the gamma distribution
The main goal of this paper is to study the accuracy of approximation for the distributions of negative-binomial random sums of independent, identically distributed random variables by the gamma distribution.
On the adaptive wavelet estimation of a multidimensional regression function under -mixing dependence: Beyond the standard assumptions on the noise
We investigate the estimation of a multidimensional regression function from observations of an -mixing process , where , represents the design and the noise. We concentrate on wavelet methods. In most papers considering this problem, either the proposed wavelet estimator is not adaptive (i.e., it depends on the knowledge of the smoothness of in its construction) or it is supposed that is bounded or/and has a known distribution. In this paper, we go far beyond this classical framework....