Related papers: An autoregressive model leading to stable distribu…

The structure of stationary first order max-autoregressive schemes with max-semi-stable marginals is studied. A connection between semi-selfsimilar extremal processes and this max-autoregressive scheme is discussed resulting in their…

We examine a random model consisting of objects with positive weights and evolving in discrete time steps, which generalizes certain random graph models. We prove almost sure convergence for the weight distribution and show scale-free…

For a uniform random labelled tree, we find the limiting distribution of tree parameters which are stable (in some sense) with respect to local perturbations of the tree structure. The proof is based on the martingale central limit theorem…

This paper explores mixture distributions induced by a product of the positive stable random variable and a power of another positive random variable. The paper also considers the convolution of the stable density with a gamma density.…

The central limit theorem ensures that a sum of random variables tends to a Gaussian distribution as their total number tends to infinity. However, for a class of positive random variables, we find that the sum tends faster to a log-normal…

The principle of linearized stability and instability is established for a classical model describing the spatial movement of an age-structured population with nonlinear vital rates. It is shown that the real parts of the eigenvalues of the…

For $\alpha\in (1,2)$, we present a generalized central limit theorem for $\alpha$-stable random variables under sublinear expectation. The foundation of our proof is an interior regularity estimate for partial integro-differential…

In this work, we propose \texttt{TimeGrad}, an autoregressive model for multivariate probabilistic time series forecasting which samples from the data distribution at each time step by estimating its gradient. To this end, we use diffusion…

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…

The question of the local stability of the (replica-symmetric) amorphous solid state is addressed for a class of systems undergoing a continuous liquid to amorphous-solid phase transition driven by the effect of random constraints. The…

In this work, we investigate the use of normalizing flows to model conditional distributions. In particular, we use our proposed method to analyze inverse problems with invertible neural networks by maximizing the posterior likelihood. Our…

In some fields of applications of stable distributions, especially in economics, it appears, that data have distributions similar to stable in a large region, but do not have such heavy tails. Our aim in this note is to propose several…

This paper is inspired by the problem of understanding in a mathematical sense the Liouville quantum gravity on surfaces. Here we show how to define a stationary random metric on self-similar spaces which are the limit of nice finite…

It is shown that asymmetric waveguides with gain and loss can support a stable propagation of optical beams. This means that the propagation constants of modes of the corresponding complex optical potential are real. A class of such…

In this work we introduce the class of beta autoregressive fractionally integrated moving average models for continuous random variables taking values in the continuous unit interval $(0,1)$. The proposed model accommodates a set of…

We generalize stochastic subgradient descent methods to situations in which we do not receive independent samples from the distribution over which we optimize, but instead receive samples that are coupled over time. We show that as long as…

We study a reaction-diffusion equation with an integral term describing nonlocal consumption of resources. We show that a homogeneous equilibrium can lose its stability resulting in appearance of stationary spatial structures. It is a new…

For regularized distributions we establish stability of the characterization of the normal law in Cramer's theorem with respect to the total variation norm and the entropic distance. As part of the argument, Sapogov-type theorems are…

In this paper, we develop a retrofit control method with approximate environment modeling. Retrofit control is a modular control approach for a general stable network system whose subsystems are supposed to be managed by their corresponding…

Normalizing Flows are generative models which produce tractable distributions where both sampling and density evaluation can be efficient and exact. The goal of this survey article is to give a coherent and comprehensive review of the…