Related papers: Large Deviation Results for the Nonparametric Regr…

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex…

We describe large deviations for normalized multiple iterated sums and integrals of the form $\bbS_N^{(\nu)}(t)=N^{-\nu}\sum_{0\leq k_1<...<k_\nu\leq Nt}\xi(k_1)\otimes\cdots\otimes\xi(k_\nu)$, $t\in[0,T]$ and…

Functional data analysis is a growing research field as more and more practical applications involve functional data. In this paper, we focus on the problem of regression and classification with functional predictors: the model suggested…

Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$\Theta_{\epsilon}(t)=\int_0^t\theta_{\epsilon}(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where…

This paper focuses on systems of nonlinear second-order stochastic differential equations with multi-scales. The motivation for our study stems from mathematical physics and statistical mechanics, for examples, Langevin dynamics and…

We prove large deviation principles for two versions of fractional Poisson processes. Firstly we consider the main version which is a renewal process; we also present large deviation estimates for the ruin probabilities of an insurance…

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $\sigma$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the…

In the present paper we obtain fully explicit large deviation inequalities for empirical processes indexed by a Vapnik--Chervonenkis class of sets (or functions). Furthermore we illustrate the importance of such results for the theory of…

In this article we prove large deviations principles for high minima of Gaussian processes with nonnegatively correlated increments on arbitrary intervals. Furthermore, we prove large deviations principles for the increments of such…

Let $M_{l,n}$ be the number of blocks with frequency $l$ in the exchangeable random partition induced by a sample of size $n$ from the Ewens-Pitman sampling model. We show that, as $n$ tends to infinity, $n^{-1}M_{l,n}$ satisfies a large…

We establish large deviation principle (LDP) for the family of vector-valued random processes $(X^\epsilon,Y^\epsilon),\epsilon\to 0$ defined as $$ X^\epsilon_t=\frac{1}{\epsilon^\kappa}\int_0^t H(\xi^\epsilon_s,Y^\epsilon_s)ds,…

Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…

We give a new large deviation inequality for sums of random variables of the form $Z_k = f(X_k,X_t)$ for $k,t\in \mathbb{N}$, $t$ fixed, where the underlying process $X$ is $\beta$-mixing. The inequality can be used to derive concentration…

Motivated by the theory of large deviations, we introduce a class of non-negative non-linear functionals that have a variational "rate function" representation.

The large deviations principle for the empirical measure for both continuous and discrete time Markov processes is well known. Various expressions are available for the rate function, but these expressions are usually as the solution to a…

We consider the recursive estimation of a regression functional where the explanatory variables take values in some functional space. We prove the almost sure convergence of such estimates for dependent functional data. Also we derive the…

In this paper we study the Large Deviation Principle (LDP in abbreviation) for a class of Stochastic Partial Differential Equations (SPDEs) in the whole space $\mathbb{R}^d$, with arbitrary dimension $d\geq 1$, under random influence which…

In practice functional data are sampled on a discrete set of observation points and often susceptible to noise. We consider in this paper the setting where such data are used as explanatory variables in a regression problem. If the primary…

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…

A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded.…