scholarly journals On Strong Bounds of Rate of Convergence for Regenerative Processes

Author(s):  
Galina Zverkina
1986 ◽  
Vol 23 (04) ◽  
pp. 1019-1024
Author(s):  
Walter Van Assche

The limit of a product of independent 2 × 2 stochastic matrices is given when the entries of the first column are independent and have the same symmetric beta distribution. The rate of convergence is considered by introducing a stopping time for which asymptotics are given.


2018 ◽  
Vol 17 (3) ◽  
pp. 172-183 ◽  
Author(s):  
Jan Cendelin ◽  
Hiroshi Mitoma ◽  
Mario Manto

Background & Objective: Neurotransplantation has been recently the focus of interest as a promising therapy to substitute lost cerebellar neurons and improve cerebellar ataxias. However, since cell differentiation and synaptic formation are required to obtain a functional circuitry, highly integrated reproduction of cerebellar anatomy is not a simple process. Rather than a genuine replacement, recent studies have shown that grafted cells rescue surviving cells from neurodegeneration by exerting trophic effects, supporting mitochondrial function, modulating neuroinflammation, stimulating endogenous regenerative processes, and facilitating cerebellar compensatory properties thanks to neural plasticity. On the other hand, accumulating clinical evidence suggests that the self-recovery capacity is still preserved even if the cerebellum is affected by a diffuse and progressive pathology. We put forward the period with intact recovery capacity as “restorable stage” and the notion of reversal capacity as “cerebellar reserve”. Conclusion: The concept of cerebellar reserve is particularly relevant, both theoretically and practically, to target recovery of cerebellar deficits by neurotransplantation. Reinforcing the cerebellar reserve and prolonging the restorable stage can be envisioned as future endpoints of neurotransplantation.


Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 880
Author(s):  
Igoris Belovas

In this research, we continue studying limit theorems for combinatorial numbers satisfying a class of triangular arrays. Using the general results of Hwang and Bender, we obtain a constructive proof of the central limit theorem, specifying the rate of convergence to the limiting (normal) distribution, as well as a new proof of the local limit theorem for the numbers of the tribonacci triangle.


2020 ◽  
Vol 20 (4) ◽  
pp. 783-798
Author(s):  
Shukai Du ◽  
Nailin Du

AbstractWe give a factorization formula to least-squares projection schemes, from which new convergence conditions together with formulas estimating the rate of convergence can be derived. We prove that the convergence of the method (including the rate of convergence) can be completely determined by the principal angles between {T^{\dagger}T(X_{n})} and {T^{*}T(X_{n})}, and the principal angles between {X_{n}\cap(\mathcal{N}(T)\cap X_{n})^{\perp}} and {(\mathcal{N}(T)+X_{n})\cap\mathcal{N}(T)^{\perp}}. At the end, we consider several specific cases and examples to further illustrate our theorems.


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