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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.
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Published in 2017 at "Communications in Mathematical Physics"
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.
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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.
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Published in 2017 at "Journal of Automated Reasoning"
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.
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Published in 2018 at "TEST"
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.
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Published in 2017 at "Food and Bioprocess Technology"
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.
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Published in 2022 at "Advances in Mathematics"
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.
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Published in 2019 at "Journal of Econometrics"
DOI: 10.1016/j.jeconom.2018.12.015
Abstract: This paper considers functional central limit theorems for stationary absolutely regular mixing processes. Bounds for the entropy with bracketing are derived using recent results in Nickl and P\"otscher (2007). More specifically, their bracketing metric entropy… read more here.
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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.
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Published in 2017 at "Journal of Statistical Planning and Inference"
DOI: 10.1016/j.jspi.2016.08.002
Abstract: Abstract For bootstrap sample sums resulting from a sequence of random variables { X n , n ≥ 1 } , a very general central limit theorem is established. The random variables { X n… read more here.
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Published in 2018 at "Journal of Statistical Planning and Inference"
DOI: 10.1016/j.jspi.2017.07.001
Abstract: Abstract Let B a , b be a weighted-fractional Brownian motion with indexes a and b satisfying | b | 1 ∧ ( 1 + a ) , a > − 1 which is a… read more here.