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most citedPrinciples alone cannot guarantee ethical AI

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Showing 2018 · math.PRShow all

6 papers · 2 filters

math.PR2018★ 24 cited

A note on the exact simulation of spherical Brownian motion

Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo

We describe an exact simulation algorithm for the increments of Brownian motion on a sphere of arbitrary dimension, based on the skew-product decomposition of the process with resp…

math.PR2018★ 11 cited

Geometrically Convergent Simulation of the Extrema of Lévy Processes

Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo

We develop a novel approximate simulation algorithm for the joint law of the position, the running supremum and the time of the supremum of a general Lévy process at an arbitrary f…

math.PR2018

The infinite Viterbi alignment and decay-convexity

Nick Whiteley, Matt W. Jones, Aleks P. F. Domanski

The infinite Viterbi alignment is the limiting maximum a-posteriori estimate of the unobserved path in a hidden Markov model as the length of the time horizon grows. For models on…

math.PR2018★ 11 cited

Exact Simulation of the Extrema of Stable Processes

Jorge Ignacio González Cázares, Aleksandar Mijatović, Gerónimo Uribe Bravo

We exhibit an exact simulation algorithm for the supremum of a stable process over a finite time interval using dominated coupling from the past (DCFTP). We establish a novel perpe…

math.PR2018★ 5 cited

Projections of spherical Brownian motion

Aleksandar Mijatović, Veno Mramor, Gerónimo Uribe Bravo

We obtain a stochastic differential equation (SDE) satisfied by the first coordinates of a Brownian motion on the unit sphere in . The SDE has non-Lipschit…

math.PR2018★ 2 cited

Invariance principle for non-homogeneous random walks

Nicholas Georgiou, Aleksandar Mijatović, Andrew R. Wade

We prove an invariance principle for a class of zero-drift spatially non-homogeneous random walks in , which may be recurrent in any dimension. The limit $\mathcal{X}…