Precise Asymptotics for Bifurcation Curve of Nonlinear Ordinary Differential Equation [PDF]
Mathematics, 2020 We study the following nonlinear eigenvalue problem −u″(t)=λf(u(t)),u(t)>0,t∈I:=(−1,1),u(±1)=0, where f(u)=log(1+u) and λ>0 is a parameter. Then λ is a continuous function of α>0, where α is the maximum norm α=∥uλ∥∞ of the solution uλ associated with λ ...
Tetsutaro Shibata
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Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball [PDF]
Abstract and Applied Analysis, 2005 We consider the semilinear elliptic eigenvalue problem −Δu+k(|x|)up=λu, u>0 in BR, u=0 on ∂BR, where p>1 is a constant, BR:={x∈RN:|x|0 is a parameter. We investigate the global structure of the branch of (λ,uλ) of bifurcation diagram from a point of view
Tetsutaro Shibata
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Precise Asymptotics for a Variable-Range Hopping Model [PDF]
Progress of Theoretical Physics Supplement, 2007 For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping
Bernhard Mehlig, Michael Wilkinson
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Precise asymptotics for Fisher–KPP fronts [PDF]
Nonlinearity, 2019 Abstract We consider the one-dimensional Fisher–KPP equation with step-like initial data. Nolen et al showed that the solution u converges at long time to a travelling wave at a position
Cole Graham
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A note on the convergence rates in precise asymptotics [PDF]
Journal of Inequalities and Applications, 2019 Let {X,Xn,n≥1} $\{X, X_{n}, n\geq1\}$ be a sequence of i.i.d. random variables with EX=0 $EX=0$, EX2=σ2 $EX^{2}=\sigma^{2}$. Set Sn=∑k=1nXk $S_{n}=\sum_{k=1}^{n}X_{k}$ and let N ${\mathcal {N} }$ be the standard normal random variable. Let g(x) $g(x)$ be
Yong Zhang
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Precise Asymptotic Generalization for Multiclass Classification with Overparameterized Linear Models [PDF]
Advances in Neural Information Processing Systems 36, 2023 NeurIPS 2023, 56 pages v3: fixed typos in sparse Hanson-Wright theorem ...
David X. Wu, Anant Sahai
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Precise asymptotics: Robust stochastic volatility models [PDF]
The Annals of Applied Probability, 2021 We present a new methodology to analyze large classes of (classical and rough) stochastic volatility models, with special regard to short-time and small noise formulae for option prices. Our main tool is the theory of regularity structures, which we use in the form of [Bayer et al; A regularity structure for rough volatility, 2017].
Peter K. Friz +2 more
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Precise asymptotics for linear mixed models with crossed random effects [PDF]
Statistical Theory and Related FieldsWe obtain an asymptotic normality result that reveals the precise asymptotic behaviour of the maximum likelihood estimators of parameters for a very general class of linear mixed models containing cross random effects.
Jiming Jiang +2 more
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On the Precise Asymptotics of the Constant in Friedrich's Inequality for Functions Vanishing on the Part of the Boundary with Microinhomogeneous Structure [PDF]
Journal of Inequalities and Applications, 2008 We construct the asymptotics of the sharp constant in the Friedrich-type inequality for functions, which vanish on the small part of the boundary Γ1ɛ. It is assumed that Γ1ɛ consists of (1/δ)n−1 pieces with diameter of order O(ɛδ
L.-E. Persson +2 more
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Precise Asymptotics on Second-Order Complete Moment Convergence of Uniform Empirical Process [PDF]
Abstract and Applied Analysis, 2014 Let {ξi,1≤i≤n} be a sequence of iid U[0, 1]-distributed random variables, and define the uniform empirical process Fn(t)=n-1/2∑i=1n(I{ξi≤t}-t),0≤t≤1, Fn=sup0≤t≤1|Fn(t)|.
Junshan Xie, Lin He
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