All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1

Displaying 1 – 19 of 19

Showing per page

On a class of linear models.

Radu Theodorescu (1985)

Trabajos de Estadística e Investigación Operativa

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 Paszkiewicz-type criterion for a.e. continuity of processes in L p -spaces

Jakub Olejnik (2010)

Banach Center Publications

In this paper we consider processes Xₜ with values in L p , p ≥ 1 on subsets T of a unit cube in ℝⁿ satisfying a natural condition of boundedness of increments, i.e. a process has bounded increments if for some non-decreasing f: ℝ₊ → ℝ₊ ||Xₜ-Xₛ||ₚ ≤ f(||t-s||), s,t ∈ T. We give a sufficient criterion for a.s. continuity of all processes with bounded increments on subsets of a given set T. This criterion turns out to be necessary for a wide class of functions f. We use a geometrical Paszkiewicz-type...

On the rate of convergence in the weak invariance principle for dependent random variables with applications to Markov chains

Ion Grama, Émile Le Page, Marc Peigné (2014)

Colloquium Mathematicae

We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is controlled by an assumption on the characteristic function of the finite-dimensional increments of the process. The distinctive feature of the new mixing condition is that the dependence increases exponentially in the dimension of the increments. The proposed mixing...

On the supremum of random Dirichlet polynomials

Mikhail Lifshits, Michel Weber (2007)

Studia Mathematica

We study the supremum of some random Dirichlet polynomials D N ( t ) = ∑ n = 2 N ε ₙ d ₙ n - σ - i t , where (εₙ) is a sequence of independent Rademacher random variables, the weights (dₙ) are multiplicative and 0 ≤ σ < 1/2. Particular attention is given to the polynomials ∑ n ∈ τ ε ₙ n - σ - i t , τ = 2 ≤ n ≤ N : P ⁺ ( n ) ≤ p τ , P⁺(n) being the largest prime divisor of n. We obtain sharp upper and lower bounds for the supremum expectation that extend the optimal estimate of Halász-Queffélec, s u p t ∈ ℝ | ∑ n = 2 N ε ₙ n - σ - i t | ≈ ( N 1 - σ ) / ( l o g N ) . The proofs are entirely based on methods of stochastic processes, in particular the metric...

Currently displaying 1 – 19 of 19

Page 1