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Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients

Alina Semrau (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

We study L p convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain D ⊆ ℝd. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case D=[0,∞) new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.

Distinguishing and integrating aleatoric and epistemic variation in uncertainty quantification

Kamaljit Chowdhary, Paul Dupuis (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Much of uncertainty quantification to date has focused on determining the effect of variables modeled probabilistically, and with a known distribution, on some physical or engineering system. We develop methods to obtain information on the system when the distributions of some variables are known exactly, others are known only approximately, and perhaps others are not modeled as random variables at all.The main tool used is the duality between risk-sensitive integrals and relative entropy, and we...

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