Related papers: Limit theorems for mixed max-sum processes with re…

Let $X$ be a continuous-time strongly mixing or weakly dependent process and $T$ a renewal process independent of $X$ with inter-arrival times $\tau$. We show general conditions under which the sampled process $(X_{T_i},T_i-T_{i-1})^{\top}$…

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

In this paper, a special sequence of controlled branching processes is considered. We provide a simple set of sufficient conditions for the weak convergence of such processes to a weak solution to a kind of continuous branching processes…

We investigate branching processes in nearly degenerate varying environment, where the offspring distribution converges to the degenerate distribution at 1. Such processes die out almost surely, therefore, we condition on non-extinction or…

We obtain limit theorems for extreme residuals in linear regression model in the case of minimax estimation of parameters.

We prove distributional limit theorems and one-sided laws of the iterated logarithm for a class of positive, mixing, stationary, stochastic processes which contains those obtained from non-integrable observables over certain piecewise…

The exponential rate of convergence and the Central Limit Theorem for some Markov operators are established. The operators correspond to iterated function systems which, for example, may be used to generalize the cell cycle model given by…

In this paper, we prove convergence in distribution of Langevin processes in the overdamped asymptotics. The proof relies on the classical perturbed test function (or corrector) method, which is used both to show tightness in path space,…

Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated.…

We show a new functional limit theorem for weakly dependent regularly varying sequences of random vectors. As it turns out, the convergence takes place in the space of R^d valued c\`{a}dl\`{a}g functions endowed with the so-called weak M1…

When the limiting compensator of a sequence of martingales is continuous, we obtain a weak convergence theorem for the martingales; the limiting process can be written as a Brownian motion evaluated at the compensator and we find sufficient…

In this paper we define the closure under weak convergence of the class of p-tempered {\alpha}-stable distributions. We give necessary and sufficient conditions for convergence of sequences in this class. Moreover, we show that any element…

Let $\{X, X_n, n\geq 1\}$ be a sequence of independent identically distributed non-degenerate random variables. Put $S_0=0, S_n = \sum^n_{i=1} X_i$ and $V_n^2=\sum^n_{i=1} X_i^2, n\ge 1.$ A weak convergence theorem is established for the…

Under the hypothesis of convergence in probability of a sequence of c\`{a}dl\`{a}g processes $(X^n)\_n$ to a c\`{a}dl\`{a}g process $X$, we are interested in the convergence of corresponding values in optimal stopping and also in the…

For a stationary sequence of random variables we derive a self-normalized functional limit theorem under joint regular variation with index $\alpha \in (0,2)$ and weak dependence conditions. The convergence takes place in the space of…

We extend a functional limit theorem for symmetric $U$-statistics [Miller and Sen, 1972] to asymmetric $U$-statistics, and use this to show some renewal theory results for asymmetric $U$-statistics. Some applications are given.

We obtain central limit theorem, local limit theorems and renewal theorems for stationary processes generated by skew product maps $T(\om,x)=(\te\om,T_\om x)$ together with a $T$-invariant measure, whose base map $\te$ satisfies certain…

Serfozo (2009, Theorem 2.65) gives a useful central limit theorem for processes with regenerative increments. Unfortunately, there is a gap in the proof. We fill this gap, and at the same time we weaken the assumptions. Furthermore, we give…

This paper deals with study of the sufficient condition of approximation raring process with mixing by renewall process. We consider use the proved results to practice problem too

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.