Semilinear stochastic partial differential equations: Central limit theorem and moderate deviations
Sign Up to like & getrecommendations! Published in 2021 at "Mathematical Methods in the Applied Sciences"
DOI: 10.1002/mma.7224
Abstract: In this paper, we establish a central limit theorem (CLT) and the moderate deviation principles (MDP) for a class of semilinear stochastic partial differential equations driven by multiplicative noise on a bounded domain. The main… read more here.
Keywords: partial differential; semilinear stochastic; central limit; stochastic partial ... See more keywords
Szegő Limit Theorem for Truncated Toeplitz Operators
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DOI: 10.1007/s00020-025-02793-y
Abstract: We discuss generalizations of the Szegő Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems. The first… read more here.
Keywords: theorem truncated; limit theorem; toeplitz operators; szeg limit ... See more keywords
A Spectral Approach for Quenched Limit Theorems for Random Expanding Dynamical Systems
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DOI: 10.1007/s00220-017-3083-7
Abstract: We prove quenched versions of (i) a large deviations principle (LDP), (ii) a central limit theorem (CLT), and (iii) a local central limit theorem for non-autonomous dynamical systems. A key advance is the extension of… read more here.
Keywords: sigma omega; limit; central limit; limit theorem ... See more keywords
On dynamic spectral risk measures, a limit theorem and optimal portfolio allocation
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DOI: 10.1007/s00780-017-0339-1
Abstract: In this paper, we propose the notion of continuous-time dynamic spectral risk measure (DSR). Adopting a Poisson random measure setting, we define this class of dynamic coherent risk measures in terms of certain backward stochastic… read more here.
Keywords: risk; time; dynamic spectral; limit theorem ... See more keywords
Central Limit Theorem and Moderate Deviations for a Class of Semilinear Stochastic Partial Differential Equations
Sign Up to like & getrecommendations! Published in 2020 at "Acta Mathematica Scientia"
DOI: 10.1007/s10473-020-0518-6
Abstract: In this paper we prove a central limit theorem and a moderate deviation principle for a class of semilinear stochastic partial differential equations, which contain the stochastic Burgers’ equation and the stochastic reaction-diffusion equation. The… read more here.
Keywords: theorem moderate; central limit; semilinear stochastic; stochastic partial ... See more keywords
A Formally Verified Proof of the Central Limit Theorem
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DOI: 10.1007/s10817-017-9404-x
Abstract: We describe a proof of the Central Limit Theorem that has been formally verified in the Isabelle proof assistant. Our formalization builds upon and extends Isabelle’s libraries for analysis and measure-theoretic probability. The proof of… read more here.
Keywords: formally verified; theorem; central limit; limit theorem ... See more keywords
Weak limit theorem for a nonlinear quantum walk
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DOI: 10.1007/s11128-018-1981-z
Abstract: This paper continues the study of large time behavior of a nonlinear quantum walk begun in Maeda et al. (Discrete Contin Dyn Syst 38:3687–3703, 2018). In this paper, we provide a weak limit theorem for… read more here.
Keywords: quantum walk; quantum; weak limit; limit theorem ... See more keywords
A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test
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DOI: 10.1007/s11749-017-0575-x
Abstract: We establish a joint central limit theorem for sums of squares and the fourth powers of residuals in a high-dimensional regression model. We then apply this CLT to detect the existence of heteroscedasticity for linear… read more here.
Keywords: high dimensional; regression; theorem sums; residuals high ... See more keywords
Application of a Model Based on the Central Limit Theorem to Predict Growth of Pseudomonas spp. in Fish Meat
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DOI: 10.1007/s11947-017-1939-7
Abstract: The purpose of this research was to develop an alternative approach to construct a primary model to describe microbial growth. This method was based on the use of the Central Limit Theorem to provide a… read more here.
Keywords: central limit; pseudomonas spp; model; growth pseudomonas ... See more keywords
A Central Limit Theorem for inner functions
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DOI: 10.1016/j.aim.2022.108318
Abstract: A Central Limit Theorem for linear combinations of iterates of an inner function is proved. The main technical tool is Aleksandrov Desintegration Theorem for Aleksandrov-Clark measures. read more here.
Keywords: inner functions; theorem; theorem inner; central limit ... See more keywords
A counterexample to the existence of a general central limit theorem for pairwise independent identically distributed random variables
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2021.124982
Abstract: Abstract The classical Central Limit Theorem (CLT) is one of the most fundamental results in statistics. It states that the standardized sample mean of a sequence of n mutually independent and identically distributed random variables… read more here.
Keywords: limit theorem; pairwise; central limit; random variables ... See more keywords