A note on the invariance principle of the product of sums of random variables.
A note on the k-th distance random variables
A note on the L1-convergence of a superadditive bisexual Galton-Watson process.
A note on the martingale central limit theorem
A note on the martingale inequality.
A Note on the Men'shov-Rademacher Inequality
We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, for all orthogonal random variables X₁,..., Xₙ such that .
A note on the optimal replacement policy
A system with a single activated unit, which can be in a finite number of states, is considered. Inspections of the system are carried out at discrete time instants. It is possible to replace it by a new one at these moments. The user of the system, by setting down conditions of replacements, wants to maximize his gain, which does not include the rest value of units. On a numerical example it is shown that the frequency of replacements of the unit need not be the greater the longer is the period...
A note on the Poisson disorder problem
A Note on the Product of Random Elements of a Semigroup.
A note on the rate of complete convergence for maximums of partial sums for moving average processes in Rademacher type Banach spaces.
A note on the rate of complete convergence for weighted sums of arrays of Banach space valued random elements.
A note on the Runge-Kutta method for stochastic differential equations
In the paper the convergence of a mixed Runge--Kutta method of the first and second orders to a strong solution of the Ito stochastic differential equation is studied under a monotonicity condition.
A note on the strong consistency of least squares estimates
The strong consistency of least squares estimates in multiples regression models with i.i.d. errors is obtained under assumptions on the design matrix and moment restrictions on the errors.
A note on the strong law of large numbers for associated sequences.
A note on the tail accuracy of the univariate saddlepoint approximation
A note on the two-sided regulated random walk
A note on the upper bounds for the dispersion.
A note on the weak convergence of probability measures on
A note on weak convergence on martingale measures
A note on weak solutions to stochastic differential equations
We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner.