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A hidden Markov model with trends is a hidden Markov model whose emission distributions are translated by a trend that depends on the current hidden state and on the current time. Contrary to standard hidden Markov models, such processes…
The theory of stochastic approximations form the theoretical foundation for studying convergence properties of many popular recursive learning algorithms in statistics, machine learning and statistical physics. Large deviations for…
We consider a system of classical particles confined in a box $\Lambda\subset\mathbb{R}^d$ with zero boundary conditions interacting via a stable and regular pair potential. Based on the validity of the cluster expansion for the canonical…
In this article, we establish the Freidlin-Wentzell type large deviation principle and central limit theorem for stochastic fractional conservation laws with small multiplicative noise in kinetic formulation framework. The weak convergence…
We show analytically how the fluctuations (i.e. standard deviation) in the Minority Game (MG) can decrease below the random coin-toss limit if the agents use more general, stochastic strategies. This suppression of the standard deviation…
Suppose that $X_1,X_2,\ldots$ are a stream of independent, identically distributed Poisson random variables with mean $\mu$. This work presents a new estimate $\mu_k$ for $\mu$ with the property that the distribution of the relative error…
We establish a moderate deviation principle (MDP) for the number of eigenvalues of a Wigner matrix in an interval. The proof relies on fine asymptotics of the variance of the eigenvalue counting function of GUE matrices due to Gustavsson.…
The classical multivariate extreme-value theory concerns the modeling of extremes in a multivariate random sample, suggesting the use of max-stable distributions. In this work, the classical theory is extended to the case where aggregated…
We consider a $\mathbb{R}^d$-valued branching random walk with a stationary and ergodic environment $\xi=(\xi_n)$ indexed by time $n\in\mathbb{N}$. Let $Z_n$ be the counting measure of particles of generation $n$. With the help of the…
By extending the methods in Peligrad et al. (2014a, b), we establish exact moderate and large deviation asymptotics for linear random fields with independent innovations. These results are useful for studying nonparametric regression with…
A moderate deviation principle as well as moderate and large deviation inequalities for a sequence of elements living inside a fixed Wiener chaos associated with an isonormal Gaussian process are shown. The conditions under which the…
We establish a central limit theorem and prove a moderate deviation principle for stochastic scalar conservation laws. Due to the lack of viscous term, this is done in the framework of kinetic solution. The weak convergence method and…
Classical works of Kac, Salem and Zygmund, and Erd\H{o}s and G\'{a}l have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random…
Consider a supercritical Crump--Mode--Jagers process $(\mathcal Z_t^{\varphi})_{t \geq 0}$ counted with a random characteristic $\varphi$. Nerman's celebrated law of large numbers [Z. Wahrsch. Verw. Gebiete 57, 365--395, 1981] states that,…
Limit theorems, including the large deviation principle, are established for random point processes (fields), which describe the position distributions of the perfect boson gas in the regime of the Bose-Einstein condensation. We compare…
In this paper we are concerned with hitting times of a family of density-dependent Markov chains. A moderate deviation principle of the hitting time is given. The proof of the main theorem relies heavily on moderate deviations of…
The standard Large Deviation Theory (LDT) is mathematically illustrated by the Boltzmann-Gibbs factor which describes the thermal equilibrium of short-range-interacting many-body Hamiltonian systems, the velocity distribution of which is…
The Poisson distribution of order $k$ is a special case of a compound Poisson distribution. Its mean and variance are known, but results for its median and mode are difficult to obtain, although a few cases have been solved and upper/lower…
A central limit theorem is shown for moderately interacting particles in the whole space. The interaction potential approximates singular attractive or repulsive potentials of sub-Coulomb type. It is proved that the fluctuations become…
This article is concerned with moderate deviation principles of a general class of mean eld type interacting particle models. We discuss functional moderate deviations of the occupation measures for both the strong -topology on the space of…