Inverspositive Operatoren und Taubersätze in der Erneuerungstheorie.
Limit distribution of the time of coincidence in renewal streams
Limit Theorems for Regenerative Excursion Processes
This work is supported by Bulgarian NFSI, grant No. MM–704/97The regenerative excursion process Z(t), t = 0, 1, 2, . . . is constructed by two independent sequences X = {Xi , i ≥ 1} and Z = {Ti , (Zi (t), 0 ≤ t < Ti ), i ≥ 1}. For the embedded alternating renewal process, with interarrival times Xi – the time for the installation and Ti – the time for the work, are proved some limit theorems for the spent worktime and the residual worktime, when at least one of the means of Xi and Ti is infinite. ...
Limiting curlicue measures for theta sums
We consider the ensemble of curves {γα, N: α∈(0, 1], N∈ℕ} obtained by linearly interpolating the values of the normalized theta sum N−1/2∑n=0N'−1exp(πin2α), 0≤N'<N. We prove the existence of limiting finite-dimensional distributions for such curves as N→∞, when α is distributed according to any probability measure λ, absolutely continuous w.r.t. the Lebesgue measure on [0, 1]. Our Main Theorem generalizes a result by Marklof [Duke Math. J.97 (1999) 127–153] and Jurkat and van Horne [Duke...
Martin boundaries associated with a killed random walk
Models of Alternating Renewal Process at Discrete Time
We study a class of models used with success in the modelling of climatological sequences. These models are based on the notion of renewal. At first, we examine the probabilistic aspects of these models to afterwards study the estimation of their parameters and their asymptotical properties, in particular the consistence and the normality. We will discuss for applications, two particular classes of alternating renewal processes at discrete time. The first class is defined by laws of sojourn time...
Moment measures of heavy-tailed renewal point processes: asymptotics and applications
We study higher-order moment measures of heavy-tailed renewal models, including a renewal point process with heavy-tailed inter-renewal distribution and its continuous analog, the occupation measure of a heavy-tailed Lévy subordinator. Our results reveal that the asymptotic structure of such moment measures are given by explicit power-law density functions. The same power-law densities appear naturally as cumulant measures of certain Poisson and Gaussian stochastic integrals. This correspondence...
Moments of passage times for Lévy processes
Necessary and sufficient optimality conditions for average reward of controlled Markov chains
On a rarefied renewal process
On coincidences in renewal streams
On fully coupled continuous time random walks
Continuous time random walks with jump sizes equal to the corresponding waiting times for jumps are considered. Sufficient conditions for the weak convergence of such processes are established and the limiting processes are identified. Furthermore one-dimensional distributions of the limiting processes are given under an additional assumption.
On limit distribution theorems for sums of a random number of random variables appearing in the study of rarefaction of a recurrent process
On moments for branching processes
On quenched and annealed critical curves of random pinning model with finite range correlations
This paper focuses on directed polymers pinned at a disordered and correlated interface. We assume that the disorder sequence is a -order moving average and show that the critical curve of the annealed model can be expressed in terms of the Perron–Frobenius eigenvalue of an explicit transfer matrix, which generalizes the annealed bound of the critical curve for i.i.d. disorder. We provide explicit values of the annealed critical curve for and and a weak disorder asymptotic in the general case....
On the extreme gap in the renewal process
On the level crossing of multi-dimensional delayed renewal processes.
On the non-equivalence of two criteria of comparability of stationary point processes
On the Taylor coefficients of the composition of two analytic functions.
On truncations for weakly ergodic inhomogeneous birth and death processes