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At the same time, it should be asserted that the discrete setup is well posed.
These two notions can be adapted to a discrete setup.
In a discrete setup, the measurement-signal relationship at time t is (A.1) y t = F u t, t = 1, …, T, where F ∈ ℂ m × n denotes a downsampled Fourier transform (FT) along the phase-encoding direction, y t ∈ ℂ m denotes the k space measurement vectors, u t ∈ ℂ n denotes the image vector at time t, and T denotes the number of time frames.
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The main aim of this paper is the converse question for the discrete multivariate setup.
We focus on discrete time setup, since most of the existing literature on this topic is dedicated to this case.
Acciaio et al. (2012) give a comprehensive study of various forms of time consistency for dynamic convex risk measures in a discrete time setup.
In the present work, we focus our attention on the discrete time setup, although we briefly review the literature devoted to continuous time.
We start with the literature review relevant to the dynamic risk and performance measures focusing on the time consistency property in the discrete time setup.
In this work we give a comprehensive overview of the time consistency property of dynamic risk and performance measures, focusing on a the discrete time setup.
Weber (2006) continues the study of dynamic convex risk measures for random variables in a discrete time setup and introduces weaker notions of time consistency acceptance and rejection time consistency.
Cheridito and Kupper (2011) introduce the notion of aggregators and generators for dynamic convex risk measures and give a thorough discussion about the composition of time-consistent convex risk measures in the discrete time setup, for both random variables and stochastic processes.
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