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Sampling and Change of Measure for Monte Carlo Integration on Simplices
Simplices are the fundamental domain when integrating over convex polytopes. The aim of this work is to establish a novel framework of Monte Carlo...
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Angle Measure
Like area measure, angle measure is a construct that can either be primitive or defined.
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Scaled insurance cash flows: representation and computation via change of measure techniques
We consider general multi-state life insurance payment processes and study the expected accumulated cash flows that arise when modifying the payments...
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Convergence of Bergman measures towards the Zhang measure
We prove that the Bergman measure along a holomorphic family of curves parametrized by the punctured unit disk converges to the Zhang measure on the...
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Change of Variables
This short chapter is devoted to the change of variables formula, which identifies the pushforward of Lebesgue measure on an open set of...
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Topological aspects of the space of metric measure spaces
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces...
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A measure-theoretic representation of graphs
Inspired by the notion of action convergence in graph limit theory, we introduce a measure-theoretic representation of matrices, and we use it to...
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Brown Measure of R-diagonal Operators, Revisited
We use the perspective of subordination functions to reformulate Haagerup–Schultz’s approach to the Brown measure of R-diagonal operators. This...
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Segmentation in Measure Spaces
We consider an abstract concept of perimeter measure space as a very general framework in which one can properly consider two of the most...
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Multiplicative arithmetic functions and the generalized Ewens measure
Random integers, sampled uniformly from [1, x ], share similarities with random permutations, sampled uniformly from S n . These similarities include...
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Measure Solutions for Impulsive Systems
This chapter studies evolution equations subject to impulsive forces, considering the questions of existence and uniqueness of measure-valued...
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Dualities, Measure Concentration and Transportation
In these three lectures we shall review and discuss in detail the fascinating connection between duality transforms (mainly Legendre and polarity,...
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A level line of the Gaussian free field with measure-valued boundary conditions
In this article, we construct samples of Schramm-Loewner-evolution-like curves out of samples of the conformal loop ensemble and Poisson point...
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Measure of non-compactness and limiting interpolation with slowly varying functions
We give estimates for the measure of non-compactness of an operator interpolated by the limiting methods involving slowly varying functions. As...
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Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps
In this paper, we study the Sinai–Ruelle–Bowen (SRB) measures of generalized horseshoe maps. We prove that under the conditions of transversality and...
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A New Risk Measure MMVaR: Properties and Empirical Research
The paper presents the properties of an alternative method, which measures market risk over time-horizon exceeding one day: Mark to market value at...
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Vague Convergence and Change of Group Law
This short chapter is devoted to a key technical result which consists in passing from the vague convergence of the family of rescaled measures...
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Tanaka Formula and Local Time for a Class of Interacting Branching Measure-valued Diffusions
We construct superprocesses with dependent spatial motion (SDSMs) in Euclidean spaces ℝ d with d ≥ 1 and show that, even when they start at some...