相关论文: Large deviation asymptotics for continued fraction…
We investigate the fluctuations of cumulative density of particles in the asymmetric simple exclusion process with respect to the stationary distribution (also known as the steady state), as a stochastic process indexed by $[0,1]$. In three…
We study the asymptotic behavior of random time changes of dynamical systems. As random time changes we propose three classes which exhibits different patterns of asymptotic decays. The subordination principle may be applied to study the…
In this paper we study the asymptotic theory for quadratic variation of a harmonizable fractional $\al$-stable process. We show a law of large numbers with a non-ergodic limit and obtain weak convergence towards a L\'evy-driven Rosenblatt…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
We obtain the rate function for the level 2.5 of large deviations for pure jump and diffusion processes. This result is proved by two methods: tilting, for which a tilted process with an appropriate typical behavior is considered, and a…
The aim of the present paper is to extend the large deviation with discontinuous statistics studied in \cite{BDE} to the diffusion $d\mathbf{x}^\varepsilon = -\{\mathbf{A}^\top (\mathbf{A} \mathbf{x}^\varepsilon - \mathbf{y}) + \mu…
A large deviation principle is derived for stochastic partial differential equations with slow-fast components. The result shows that the rate function is exactly that of the averaged equation plus the fluctuating deviation which is a…
We establish some asymptotic expansions for infinite weighted convolution of distributions having regular varying tails. Various applications to statistics and probability are developed.
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
The system of equations for parametric sub-resonant growth of the amplitude of oscillations was obtained. The time of turning point from the growing of the amplitude to the bounded oscillations in the slow variable was found. The comparison…
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…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We give an exponential upper bound on the probabilitywith which the denominator of the $n$th convergent in the regular continued fraction expansion stays away from the mean $\frac{n\pi^2}{12\log2}$. The exponential rate is best possible,…
In this paper, some global existence and uniform asymptotic stability results for fractional functional differential equations are proved. It is worthy mentioning that when $\alpha=1$ the initial value problem (1.1) reduces to a classical…
We study the upper tail behaviors of the local times of the additive stable processes. Let $X_1(t),...,X_p(t)$ be independent, d-dimensional symmetric stable processes with stable index $0<\alpha\le 2$ and consider the additive stable…
In a growth-fragmentation system, cells grow in size slowly and split apart at random. Typically, the number of cells in the system grows exponentially and the distribution of the sizes of cells settles into an equilibrium 'asymptotic…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
We consider a sequence of processes defined on half-line for all non negative t. We give sufficient conditions for Large Deviation Principle (LDP) to hold in the space of continuous functions with a new metric that is more sensitive to…
We investigate the problem of the distribution of sums of functions of prime numbers located on an arithmetic progression. This problem is closely related to the problem of the distribution of prime numbers on an arithmetic progression.…