Related papers: Instantons for rare events in heavy-tailed distrib…
Accurate and efficient estimation of rare events probabilities is of significant importance, since often the occurrences of such events have widespread impacts. The focus in this work is on precisely quantifying these probabilities, often…
We study large deviation probabilities for a sum of dependent random variables from a heavy-tailed factor model, assuming that the components are regularly varying. We identify conditions where both the factor and the idiosyncratic terms…
We study inference on the common stochastic trends in a non-stationary, $N$-variate time series $y_{t}$, in the possible presence of heavy tails. We propose a novel methodology which does not require any knowledge or estimation of the tail…
This paper introduces novel frameworks for large deviations and metastability analysis in heavy-tailed stochastic dynamical systems. We develop and apply these frameworks within the context of stochastic difference equation $X^\eta_{j+1}(x)…
Freidlin-Wentzell theory of large deviations can be used to compute the likelihood of extreme or rare events in stochastic dynamical systems via the solution of an optimization problem. The approach gives exponential estimates that often…
Understanding intermittency of turbulent systems from the underlying differential equations is an outstanding problem in fluid dynamics. Here, in the example of Burgers turbulence as a stringent test, we introduce a method that yields…
We consider a class of chance-constrained programs in which profit needs to be maximized while enforcing that a given adverse event remains rare. Using techniques from large deviations and extreme value theory, we show how the optimal value…
We present here a simple method for computing the large deviation of long time average for stochastic jump processes. We show that the computation of the rate function can be reduced to that of a partial differential equation governing the…
We describe an adaptive importance sampling algorithm for rare events that is based on a dual stochastic control formulation of a path sampling problem. Specifically, we focus on path functionals that have the form of cumulate generating…
We consider the tails of probability density functions (PDF) for different characteristics of velocity that satisfies Burgers equation driven by a large-scale force. The saddle-point approximation is employed in the path integral so that…
The prediction and control of rare events is an important task in disciplines that range from physics and biology, to economics and social science. The Big Jump principle deals with a peculiar aspect of the mechanism that drives rare…
We outline a strategy of how to search for QCD instantons of invariant mass 20 -- 60 GeV in diffractive events in low luminosity runs at the LHC. We show that by imposing appropriate selection criteria on the final states, one can select…
Establishing a Large Deviation Principle (LDP) proves to be a powerful result for a vast number of stochastic models in many application areas of probability theory. The key object of an LDP is the large deviations rate function, from which…
We develop a novel procedure for estimating the optimizer of general convex stochastic optimization problems of the form $\min_{x\in\mathcal{X}} \mathbb{E}[F(x,\xi)]$, when the given data is a finite independent sample selected according to…
Extreme events and the heavy tail distributions driven by them are ubiquitous in various scientific, engineering and financial research. They are typically associated with stochastic instability caused by hidden unresolved processes.…
The theory of large deviations deals with the probabilities of rare events (or fluctuations) that are exponentially small as a function of some parameter, e.g., the number of random components of a system, the time over which a stochastic…
We consider the problem of choosing design parameters to minimize the probability of an undesired rare event that is described through the average of $n$ iid random variables. Since the probability of interest for near optimal design…
Assessing the probability of occurrence of extreme events is a crucial issue in various fields like finance, insurance, telecommunication or environmental sciences. In a multivariate framework, the tail dependence is characterized by the…
In this paper we develop a perturbation method to predict the rate of occurrence of rare events for singularly perturbed stochastic systems using a probability density function approach. In contrast to a stochastic normal form approach, we…
Rare event simulation and rare event probability estimation are important tasks within the analysis of systems subject to uncertainty and randomness. Simultaneously, accurately estimating rare event probabilities is an inherently difficult…