Related papers: Uniform bounds for ruin probability in Multidimens…
In the paper, we investigate the asymptotic behaviors of the randomly weighted sums with upper tail asymptotically independent increments under new conditions without requiring moment assumptions on random weights.An application of the…
In this paper, we consider a bidimensional renewal risk model with constant force of interest, in which the claim size vector with certain local subexponential marginal distribution and its inter-arrival time are subject to a new…
We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing…
This paper extends the standard chaining technique to prove excess risk upper bounds for empirical risk minimization with random design settings even if the magnitude of the noise and the estimates is unbounded. The bound applies to many…
An asymptotic method for finding instabilities of arbitrary $d$-dimensional large-amplitude patterns in a wide class of reaction-diffusion systems is presented. The complete stability analysis of 2- and 3-dimensional localized patterns is…
We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk…
Uniform large deviation principles for positive functionals of all equivalent types of infinite dimensional Brownian motions acting together with a Poisson random measure are established. The core of our approach is a variational…
A convenient framework for dealing with asymptotic limit problems of probabilistic nature is provided. These problems include questions such as finding the asymptotic proportion of terms of a sequence falling inside a given interval, or the…
We prove an invariance principle for Brownian motion in Gaussian or Poissonian random scenery by the method of characteristic functions. Annealed asymptotic limits are derived in all dimensions, with a focus on the case of dimension $d=2$,…
We obtain the distribution of the maximal average in a sequence of independent identically distributed exponential random variables. Surprisingly enough, it turns out that the inverse distribution admits a simple closed form. An application…
In two recent papers [5] and [6], we generalized some classical results of Harmonic Analysis using probabilistic approach by means of a d- dimensional rotationally symmetric stable process. These results allow one to discuss some…
We extend generalized isoperimetric-type inequalities to iterated Brownian motion over several domains in $\RR{R}^{n}$. These kinds of inequalities imply in particular that for domains of finite volume, the exit distribution and moments of…
We study the probability of ruin before time $t$ for the family of tempered stable L\'evy insurance risk processes, which includes the spectrally positive inverse Gaussian processes. Numerical approximations of the ruin time distribution…
In this paper, we derive non-asymptotic achievability and converse bounds on the random number generation with/without side-information. Our bounds are efficiently computable in the sense that the computational complexity does not depend on…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
Generalization bounds which assess the difference between the true risk and the empirical risk have been studied extensively. However, to obtain bounds, current techniques use strict assumptions such as a uniformly bounded or a Lipschitz…
This paper presents a novel model for bivariate stochastic fluid processes that incorporate a ruin-dependent behavioral switch. Unlike typical models that assume a shared underlying process, our model allows each process to operate…
If a given aggregate process $S$ is a compound mixed renewal process under a probability measure $P$, we provide a characterization of all probability measures $Q$ on the domain of $P$ such that $Q$ and $P$ are progressively equivalent and…
The Chernoff bound is a well-known tool for obtaining a high probability bound on the expectation of a Bernoulli random variable in terms of its sample average. This bound is commonly used in statistical learning theory to upper bound the…
We construct the least-square estimator for the unknown drift parameter in the multifractional Ornstein-Uhlenbeck model and establish its strong consistency in the non-ergodic case. The proofs are based on the asymptotic bounds with…