Related papers: Instantons for rare events in heavy-tailed distrib…

Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient…

Processes leading to anomalous fluctuations in turbulent flows, referred to as intermittency, are still challenging. We consider cascade trajectories through scales as realizations of a stochastic Langevin process for which multiplicative…

For many non-equilibrium dynamics driven by small noise, in physics, chemistry, biology, or economy, rare events do matter. Large deviation theory then explains that the leading order term of the main statistical quantities have an…

Standard statistical analysis is unable to provide reliable confidence intervals on expectation values of probability distributions that do not satisfy the conditions of the central limit theorem. We present a regression-based estimator of…

This study investigates, by means of numerical simulations, extreme mechanical force exerted by a turbulent flow impinging on a bluff body, and examines the relevance of two distinct rare-event algorithms to efficiently sample these events.…

We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application,…

Chance constraints provide a principled framework to mitigate the risk of high-impact extreme events by modifying the controllable properties of a system. The low probability and rare occurrence of such events, however, impose severe…

The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…

We develop an efficient simulation algorithm for computing the tail probabilities of the infinite series $S = \sum_{n \geq 1} a_n X_n$ when random variables $X_n$ are heavy-tailed. As $S$ is the sum of infinitely many random variables, any…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

We consider the problem of asynchronous stochastic optimization, where an optimization algorithm makes updates based on stale stochastic gradients of the objective that are subject to an arbitrary (possibly adversarial) sequence of delays.…

First-passage probability estimation of high-dimensional nonlinear stochastic systems is a significant task to be solved in many science and engineering fields, but remains still an open challenge. The present paper develops a novel…

Importance sampling algorithms for heavy-tailed random walks are considered. Using a specification with algorithms based on mixtures of the original distribution with some other distribution, sufficient conditions for obtaining bounded…

We consider a stochastic recurrence equation of the form $Z_{n+1} = A_{n+1} Z_n+B_{n+1}$, where $\mathbb{E}[\log A_1]<0$, $\mathbb{E}[\log^+ B_1]<\infty$ and $\{(A_n,B_n)\}_{n\in\mathbb{N}}$ is an i.i.d. sequence of positive random vectors.…

Several novel statistical methods have been developed to estimate large integrated volatility matrices based on high-frequency financial data. To investigate their asymptotic behaviors, they require a sub-Gaussian or finite high-order…

Estimating the expectations of functionals applied to sums of random variables (RVs) is a well-known problem encountered in many challenging applications. Generally, closed-form expressions of these quantities are out of reach. A naive…

We provide a numerically robust and fast method capable of exploiting the local geometry when solving large-scale stochastic optimisation problems. Our key innovation is an auxiliary variable construction coupled with an inverse Hessian…

In this paper we develop a stochastic heavy ball method for solving ill-posed inverse problems. The method updates the iterate using only a randomly selected equation at each iteration step while incorporating a momentum term into the…

Large-deviations theory deals with tails of probability distributions and the rare events of random processes, for example spreading packets of particles. Mathematically, it concerns the exponential fall-of of the density of thin-tailed…

The estimation of the probability of rare events is an important task in reliability and risk assessment. We consider failure events that are expressed in terms of a limit state function, which depends on the solution of a partial…