Related papers: A supermartingale argument for characterizing the …
We determine the asymptotic distribution of the sum of correlated variables described by a matrix product ansatz with finite matrices, considering variables with finite variances. In cases when the correlation length is finite, the law of…
Asymptotic behavior of distribution functions of local quantities in disordered conductors is studied in the weak disorder limit by means of an optimal fluctuation method. It is argued that this method is more appropriate for the study of…
We study the questions of determining the asymptotics of the probabilistic characteristics of additive arithmetic functions in the paper, regardless of whether they have a limit distribution or not. Several assertions are proved about the…
The estimation of parameters in the frequency spectrum of a seasonally persistent stationary stochastic process is addressed. For seasonal persistence associated with a pole in the spectrum located away from frequency zero, a new…
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
We recently introduced a robust approach to the derivation of sharp asymptotic formula for correlation functions of statistical mechanics models in the high-temperature regime. We describe its application to the nonperturbative proof of…
We study the existence, strong consistency and asymptotic normality of estimators obtained from estimating functions, that are p-dimensional martingale transforms. The problem is motivated by the analysis of evolutionary clustered data,…
We prove the reduction principle for asymptotics of functionals of vector random fields with weakly and strongly dependent components. These functionals can be used to construct new classes of random fields with skewed and heavy-tailed…
The application of the Cauchy distribution has often been discussed as a potential model of the financial markets. In particular the way in which single extreme, or "Black Swan", events can impact long term historical moments, is often…
We derive an asymptotic expansion for the distribution of a compound sum of independent random variables, all having the same light-tailed subexponential distribution. The examples of a Poisson and geometric number of summands serve as an…
We study the asymptotic behavior of stochastic hyperbolic parabolic equations with slow and fast time scales. Both the strong and weak convergence in the averaging principe are established, which can be viewed as a functional law of large…
In this paper, the asymptotic distributions of estimators for the regularized functional canonical correlation and variates of the population are derived. The method is based on the possibility of expressing these regularized quantities as…
We discuss in detail the asymptotic distribution of sample expectiles. First, we show uniform consistency under the assumption of a finite mean. In case of a finite second moment, we show that for expectiles other then the mean, only the…
Let $\{X(t):t\in[0,\infty)\}$ be a centered Gaussian process with stationary increments and variance function $\sigma^2_X(t)$. We study the exact asymptotics of ${\mathbb{P}}(\sup_{t\in[0,T]}X(t)>u)$ as $u\to\infty$, where $T$ is an…
The article studies the almost surely asymptotics of extreme values $\bar{\xi}_n = \max_{1\leq i \leq n} \xi_i$, where $ \xi , \xi_1 , \xi_2 , \ldots$ are discrete identically distributed random variables. One of the main results on this…
A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties…
This paper considers the effect of least squares procedures for nearly unstable linear time series with strongly dependent innovations. Under a general framework and appropriate scaling, it is shown that ordinary least squares procedures…
The aim of this paper is to deepen the analysis of the asymptotic behavior of the so-called minimal random walk (MRW) using a new martingale approach. The MRW is a discrete-time random walk with infinite memory that has three regimes…
We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…