Related papers: Large deviations for a class of tempered subordina…
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples…
In the last decade the subordinated processes have become popular and found many practical applications. Therefore in this paper we examine two processes related to time-changed (subordinated) classical Brownian motion with drift (called…
In this paper, we study small noise asymptotics of Markov-modulated diffusion processes in the regime that the modulating Markov chain is rapidly switching. We prove the joint sample-path large deviations principle for the Markov-modulated…
We address the question of condensation and extremes for three classes of intimately related stochastic processes: (a) random allocation models and zero-range processes, (b) tied-down renewal processes, (c) free renewal processes. While for…
The space-fractional and the time-fractional Poisson processes are two well-known models of fractional evolution. They can be constructed as standard Poisson processes with the time variable replaced by a stable subordinator and its…
In this paper we prove large and moderate deviations principles for the recursive kernel estimator of a probability density function and its partial derivatives. Unlike the density estimator, the derivatives estimators exhibit a quadratic…
We consider a stable but nearly unstable autoregressive process of any order. The bridge between stability and instability is expressed by a time-varying companion matrix $A_{n}$ with spectral radius $\rho(A_{n}) < 1$ satisfying…
We introduce a multistable subordinator, which generalizes the stable subordinator to the case of time-varying stability index. This enables us to define a multifractional Poisson process. We study properties of these processes and…
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…
Using martingale methods, we obtain some upper bounds for large and moderate deviations of products of independent and identically distributed elements of GL d (R). We investigate all the possible moment conditions, from super-exponential…
In this paper, a method to exactly sample the trajectories of inverse subordinators (in the sense of the finite-dimensional distributions), jointly with the undershooting or overshooting process, is provided. The method applies to general…
Margin-based classifiers have been popular in both machine learning and statistics for classification problems. Since a large number of classifiers are available, one natural question is which type of classifiers should be used given a…
We consider large deviations of empirical measures of diffusion processes. In a first part, we present conditions to obtain a large deviations principle (LDP) for a precise class of unbounded functions. This provides an analogue to the…
Deep Gaussian Processes learn probabilistic data representations for supervised learning by cascading multiple Gaussian Processes. While this model family promises flexible predictive distributions, exact inference is not tractable.…
In this article, we introduce mixtures of tempered stable subordinators (TSS). These mixtures define a class of subordinators which generalize tempered stable subordinators. The main properties like probability density function (pdf), Levy…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
In this paper we introduce the concept of random time changes in dynamical systems. The subordination principle may be applied to study the long time behavior of the random time systems. We show, under certain assumptions on the class of…
In a general class of one dimensional random differential equation the convergence of the distribution function of the solution to stationary state distribution is studied. In particular it is proved the boundedness respectively the…
We study the large deviation estimates for the short time asymptotic behavior of a strongly degenerate diffusion process. Assuming a nilpotent structure of the Lie algebra generated by the driving vector fields, we obtain a graded large…
In this article, we study the potential theory of normal tempered stable process which is obtained by time-changing the Brownian motion with a tempered stable subordinator. Precisely, we study the asymptotic behavior of potential density…