Related papers: A Lundberg-type inequality for an inhomogeneous re…
We consider a class of non-homogeneous Markov chains, that contains many natural examples. Next, using martingale methods, we establish some deviation and moment inequalities for separately Lipschitz functions of such a chain, under moment…
We prove moment inequalities for a class of functionals of i.i.d. random fields. We then derive rates in the central limit theorem for weighted sums of such randoms fields via an approximation by $m$-dependent random fields.
The paper addresses the formulation and analysis of direct and inverse problems for a Langevin-type fractional differential equation under a non-local condition imposed on the time variable. An additional condition for solving the inverse…
We discuss the problem of the existence of a regular invariant Lagrangian for a given system of invariant second-order differential equations on a Lie group $G$, using approaches based on the Helmholtz conditions. Although we deal with the…
We study a class of time-inhomogeneous diffusion: the self-interacting one. We show a convergence result with a rate of convergence that does not depend on the diffusion coefficient. Finally, we establish a so-called Kramers' type law for…
In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of…
Using a sharp Gagliardo-Nirenberg type inequality, well-posedness issues of the initial value problem for a fractional inhomogeneous Schrodinger equation are investigated.
In this paper, we settle the problem for time-dependent Hartree equation with inhomogeneous boundary condition in a bounded Lipschitz domain in $\mathbb{R}^{N}$. A global existence result is derived.
We want to reconstruct a signal based on inhomogeneous data (the amount of data can vary strongly), using the model of regression with a random design. Our aim is to understand the consequences of inhomogeneity on the accuracy of estimation…
We study the susceptibility, i.e., the mean size of the component containing a random vertex, in a general model of inhomogeneous random graphs. This is one of the fundamental quantities associated to (percolation) phase transitions; in…
A growing number of applications involve settings where, in order to infer heterogeneous effects, a researcher compares various units. Examples of research designs include children moving between different neighborhoods, workers moving…
Consider an insurance company exposed to a stochastic economic environment that contains two kinds of risk. The first kind is the insurance risk caused by traditional insurance claims, and the second kind is the financial risk resulting…
We study the multiplicative hazards model with intermittently observed longitudinal covariates and time-varying coefficients. For such models, the existing ad hoc approach, such as the last value carried forward, is biased. We propose a…
An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this…
We prove Berry-Esseen theorems, almost sure invariance principle rates and large deviations for products of independent but not identically distributed invertible matrices with some average (logarithmic) projective contraction and uniform…
We adapt arguments concerning information-theoretic convergence in the Central Limit Theorem to the case of dependent random variables under Rosenblatt mixing conditions. The key is to work with random variables perturbed by the addition of…
We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak…
This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this…
The main result of the article is the rate of convergence to the Rosenblatt-type distributions in non-central limit theorems. Specifications of the main theorem are discussed for several scenarios. In particular, special attention is paid…
We contribute to the understanding of how systemic risk arises in a network of credit-interlinked agents. Motivated by empirical studies we formulate a network model which, despite its simplicity, depicts the nature of interbank markets…