Related papers: Efficient Rare-Event Simulation for Multiple Jump …

We develop a new algorithm for the estimation of rare event probabilities associated with the steady-state of a Markov stochastic process with continuous state space $\mathbb R^d$ and discrete time steps (i.e. a discrete-time $\mathbb…

Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…

We propose an effective explicit numerical scheme for simulating solutions of stochastic differential equations with confining superlinear drift terms, driven by multiplicative heavy-tailed L\'evy noise. The scheme is designed to prevent…

In many random search processes of interest in chemistry, biology or during rescue operations, an entity must find a specific target site before the latter becomes inactive, no longer available for reaction or lost. We present exact results…

The pricing of options in exponential Levy models amounts to the computation of expectations of functionals of Levy processes. In many situations, Monte-Carlo methods are used. However, the simulation of a Levy process with infinite Levy…

We study rare events in the extreme value statistics of stochastic symmetric jump processes with power tails in the distributions of the jumps, using the big-jump principle. The principle states that in the presence of stochastic processes…

L\'{e}vy processes with completely monotone jumps appear frequently in various applications of probability. For example, all popular stock price models based on L\'{e}vy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse…

Importance sampling is a variance reduction technique for efficient estimation of rare-event probabilities by Monte Carlo. In standard importance sampling schemes, the system is simulated using an a priori fixed change of measure suggested…

We develop a new Monte Carlo variance reduction method to estimate the expectation of two commonly encountered path-dependent functionals: first-passage times and occupation times of sets. The method is based on a recursive approximation of…

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…

In Part I (arXiv:1911.00619) of this article, we proposed an importance sampling algorithm to compute rare-event probabilities in forward uncertainty quantification problems. The algorithm, which we termed the "Bayesian Inverse Monte Carlo…

This paper proposes niching importance sampling, a framework that combines concepts from reliability analysis, e.g. Markov chains, importance sampling, and relative cross entropy minimisation, with niching techniques from evolutionary…

Importance sampling has been reported to produce algorithms with excellent empirical performance in counting problems. However, the theoretical support for its efficiency in these applications has been very limited. In this paper, we…

The main purpose of this chapter is to present some theoretical aspects of parametric estimation of L\'evy processes based on high-frequency sampling, with a focus on infinite activity pure-jump models. Asymptotics for several classes of…

This article focuses, in the context of epidemic models, on rare events that may possibly correspond to crisis situations from the perspective of Public Health. In general, no close analytic form for their occurrence probabilities is…

In solving simulation-based stochastic root-finding or optimization problems that involve rare events, such as in extreme quantile estimation, running crude Monte Carlo can be prohibitively inefficient. To address this issue, importance…

Rare events in stochastic processes with heavy-tailed distributions are controlled by the big jump principle, which states that a rare large fluctuation is produced by a single event and not by an accumulation of coherent small deviations.…

Large deviation theory and instanton calculus for stochastic systems are widely used to gain insight into the evolution and probability of rare events. At its core lies the realization that rare events are, under the right circumstances,…

Statistical inference for stochastic processes based on high-frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic…

We characterize the small-time asymptotic behavior of the exit probability of a L\'evy process out of a two-sided interval and of the law of its overshoot, conditionally on the terminal value of the process. The asymptotic expansions are…