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most citedPrinciples alone cannot guarantee ethical AI

1.8k citations

Showing 2020 · math.PRShow all

5 papers · 2 filters

math.PR2020★ 7 cited

Simulation of the drawdown and its duration in Lévy models via stick-breaking Gaussian approximation

Jorge González Cázares, Aleksandar Mijatović

We develop a computational method for expected functionals of the drawdown and its duration in exponential Lévy models. It is based on a novel simulation algorithm for the joint la…

math.PR2020★ 3 cited

Joint density of a stable process and its supremum: regularity and upper bounds

Jorge González Cázares, Arturo Kohatsu Higa, Aleksandar Mijatović

This article uses a combination of three ideas from simulation to establish a nearly optimal polynomial upper bound for the joint density of the stable process and its associated s…

math.PR2020★ 27 cited

Large and moderate deviations for stochastic Volterra systems

Antoine Jacquier, Alexandre Pannier

We provide a unified treatment of pathwise Large and Moderate deviations principles for a general class of multidimensional stochastic Volterra equations with singular kernels, not…

math.PR2020★ 1 cited

Recovering Brownian and jump parts from high-frequency observations of a Lévy process

Jorge González Cázares, Jevgenijs Ivanovs

We introduce two general non-parametric methods for recovering paths of the Brownian and jump components from high-frequency observations of a Lévy process. The first procedure rel…

math.PR2020★ 5 cited

Reflecting random walks in curvilinear wedges

Mikhail V. Menshikov, Aleksandar Mijatović, Andrew R. Wade

We study a random walk (Markov chain) in an unbounded planar domain whose boundary is described by two curves of the form and , with $x_…