相关论文: Laws of large numbers for Hayashi-Yoshida-type fun…

We study maximum-likelihood-type estimation for diffusion processes when the coefficients are nonrandom and observation occurs in nonsynchronous manner. The problem of nonsynchronous observations is important when we consider the analysis…

The functional delta-method provides a convenient tool for deriving the asymptotic distribution of a plug-in estimator of a statistical functional from the asymptotic distribution of the respective empirical process. Moreover, it provides a…

We derive the asymptotic behavior for an additive functional of two independent self-similar Gaussian processes when their intersection local time exists, using the method of moments.

In this paper we study the asymptotic behaviour of weighted random sums when the sum process converges stably in law to a Brownian motion and the weight process has continuous trajectories, more regular than that of a Brownian motion. We…

We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…

This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach…

In this paper, we study the asymptotic behavior of a semi-linear slow-fast stochastic partial differential equation with singular coefficients. Using the Poisson equation in Hilbert space, we first establish the strong convergence in the…

Summation arithmetic functions with asymptotically independent terms are studied in the paper, the limit of which is the law of normal distribution. Assertions about the asymptotic behavior of the indicated functions are proved.

We derive an asymptotic expansion for the quadratic variation of a stochastic process satisfying a stochastic differential equation driven by a fractional Brownian motion, based on the theory of asymptotic expansion of Skorohod integrals…

The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…

The recent experimental progresses in handling microscopic systems have allowed to probe them at levels where fluctuations are prominent, calling for stochastic modeling in a large number of physical, chemical and biological phenomena. This…

In this paper, we study inference for high-dimensional data characterized by small sample sizes relative to the dimension of the data. In particular, we provide an infinite-dimensional framework to study statistical models that involve…

In this paper, we consider asymptotic behaviors of multiscale multivalued stochastic systems with small noises. First of all, for general, fully coupled systems for multivalued stochastic differential equations of slow and fast motions with…

The aim of this note is to investigate the asymptotic stability behaviour of the Cauchy and Jensen functional equations. Our main results show that if these equations hold for large arguments with small error, then they are also valid…

The paper compares probabilistic and exact methods for estimating the asymptotic behavior of summation arithmetic functions, and estimates of the results are obtained by precise methods. Conditions for stationarity in the broad sense are…

In this paper we study the asymptotic theory for samples problem based on the functional empirical process (fep), this new method is called general samples problem. We suggest this method to develop the full theory of estimation of means,…

The paper considers estimates for the asymptotics of summation functions of bounded multiplicative arithmetic functions. Several assertions on this subject are proved and examples are considered.

This work considers the asymptotic behavior of the distance between two sample covariance matrices (SCM). A general result is provided for a class of functionals that can be expressed as sums of traces of functions that are separately…

Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…