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A Stochastic Measure for Eternal Inflation [PDF]
Journal of Cosmology and Astroparticle Physics, 2007 We use the stochastic approach to investigate the measure for slow roll eternal inflation. The probability for the universe of a given Hubble radius can be calculated in this framework.
Arkani-Hamed N Dubovsky S Nicolis A Trincherini E Villadoro G +24 more
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Transport equation driven by a stochastic measure
Modern Stochastics: Theory and Applications, 2023 The stochastic transport equation is considered where the randomness is given by a symmetric integral with respect to a stochastic measure. For a stochastic measure, only σ-additivity in probability and continuity of paths is assumed.
Vadym Radchenko
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Asymptotic properties of the parabolic equation driven by stochastic measure
Modern Stochastics: Theory and Applications, 2022 A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure, for which we assume only σ-additivity in probability, is considered. The asymptotic behavior of its solution as $t\to \infty $ is studied.
Boris Manikin
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Averaging principle for the one-dimensional parabolic equation driven by stochastic measure
Modern Stochastics: Theory and Applications, 2022 A stochastic parabolic equation on $[0,T]\times \mathbb{R}$ driven by a general stochastic measure is considered. The averaging principle for the equation is established. The convergence rate is compared with other results on related topics.
Boris Manikin
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Iterated stochastic measurements [PDF]
Journal of Physics A: Mathematical and Theoretical, 2012 We describe a measurement device principle based on discrete iterations of Bayesian updating of system state probability distributions. Although purely classical by nature, these measurements are accompanied with a progressive collapse of the system state probability distribution during each complete system measurement.
Bauer, Michel +2 more
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The Burgers equation driven by a stochastic measure
Modern Stochastics: Theory and Applications, 2023 The class of one-dimensional equations driven by a stochastic measure μ is studied. For μ only σ-additivity in probability is assumed. This class of equations includes the Burgers equation and the heat equation.
Vadym Radchenko
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Stochastically Stable Quenched Measures [PDF]
Journal of Statistical Physics, 2004 We analyze a class of stochastically stable quenched measures. We prove that stochastic stability is fully characterized by an infinite family of zero average polynomials in the covariance matrix entries.
Alessandra Bianchi +2 more
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Invariant Measure for Stochastic Schrödinger Equations [PDF]
Annales Henri Poincaré, 2021 As accepted in Ann.
Benoist, Tristan +3 more
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Coarse-Graining of Observables
Quantum Reports, 2022 We first define the coarse-graining of probability measures in terms of stochastic kernels. We define when a probability measure is part of another probability measure and say that two probability measures coexist if they are both parts of a single ...
Stan Gudder
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A maximum flow network interdiction model in fuzzy stochastic hybrid uncertainty environments [PDF]
Yugoslav Journal of Operations Research, 2023 Uncertainty is an inherent characteristic of a decision-making process. Occasionally, historical data may be insufficient to accurately estimate the probability distribution suitable for an unknown variable.
Bavandi Salim, Bigdeli Hamid
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