Related papers: Complete convergence theorem for stationary heavy …
In this paper we give simple sufficient conditions for linear type processes with short memory that imply the invariance principle. Various examples including projective criterion are considered as applications. In particular, we treat the…
We prove that several results of lineability/spaceability in the framework of sequence spaces are valid in a stricter sense.
We consider a sequence of additive functionals {\phi_n}, set on a sequence of Markov chains {X_n} that weakly converges to a Markov process X. We give sufficient condition for such a sequence to converge in distribution, formulated in terms…
Stationary points or derivative zero crossings of a regression function correspond to points where a trend reverses, making their estimation scientifically important. Existing approaches to uncertainty quantification for stationary points…
For linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0, 2)$, we study functional convergence of the joint partial sum and partial maxima processes. We derive a…
We introduce a large scale analogue of the classical fixed-point property for continuous maps, which shall apply to coarse maps. We also develop a coarse version of degree for coarse maps on Euclidean spaces. Then, applying a coarse…
We prove non-convergence theorems towards an unstable equilibrium (or a trap) for stochastic processes. The processes we consider are continuous-time or discrete-time processes and can be pertubations of the flow generated by a vector…
Rate of convergence is studied for a diffusion process on the half line with a non-sticky reflection to a heavy-tailed 1D invariant distribution which density on the half line has a polynomial decay at infinity. Starting from a standard…
We suggest an approach to obtaining general two-sided bounds on the rate of convergence in terms of special "weighted" norms related to total variation. Some important classes of continuous-time Markov chains are considered:…
This paper gives a simple proof of a limit theorem for the lenght of the largest interval straddling a fixed number of i.i.d. points uniformly disributed on a unit interval. The key step in our argument is a classical theorem of Watson…
We consider stationary time series $\{X_j, j \in Z\} whose finite dimensional distributions are regularly varying with extremal independence. We assume that for each $h \geq 1$, conditionally on $X_0$ to exceed a threshold tending to…
It is shown that as far as the linear diffusion equation meets both time- and space- translational invariance, the time dependence of a moment of degree $\alpha$ is a polynomial of degree at most equal to $\alpha$, while all connected…
The goal of this paper is to investigate the tools of extreme value theory originally introduced for discrete time stationary stochastic processes (time series), namely the tail process and the tail measure, in the framework of continuous…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian…
In this paper a general approach for the perfect simulation of a stationary process with at most countable state space is outlined. The process is specified through a kernel, prescribing the probability of each state conditional to the…
The principal results of this contribution are the weak and strong limits of maxima of contracted stationary Gaussian random sequences. Due to the random contraction we introduce a modified Berman condition which is sufficient for the weak…
This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided.…
We prove a fixpoint theorem for contractions on Cauchy-complete quantale-enriched categories. It holds for any quantale whose underlying lattice is continuous, and applies to contractions whose control function is sequentially…
We refine previous results concerning the Renewal Contact Processes. We significantly widen the family of distributions for the interarrival times for which the critical value can be shown to be strictly positive. The result now holds for…