The infinitely-many-neutral-alleles diffusion model

1981 ◽  
Vol 13 (3) ◽  
pp. 429-452 ◽  
Author(s):  
S. N. Ethier ◽  
Thomas G. Kurtz
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Order Statistics ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Stochastic Models ◽  
Dirichlet Distribution ◽  
Infinite Dimensional ◽  
Image Position ◽  
Discrete Stochastic Models

A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.

The infinitely-many-neutral-alleles diffusion model

1981 ◽  
Vol 13 (03) ◽  
pp. 429-452 ◽  
Author(s):  
S. N. Ethier ◽  
Thomas G. Kurtz
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Order Statistics ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Stochastic Models ◽  
Dirichlet Distribution ◽  
Infinite Dimensional ◽  
Image Position ◽  
Discrete Stochastic Models

A diffusion process X(·) in the infinite-dimensional ordered simplex is characterized in terms of the generator defined on an appropriate domain. It is shown that X(·) is the limit in distribution of several sequences of discrete stochastic models of the infinitely-many-neutral-alleles type. It is further shown that X(·) has a unique stationary distribution and is reversible and ergodic. Kingman's limit theorem for the descending order statistics of the symmetric Dirichlet distribution is obtained as a corollary.

Une généralisation du modèle de diffusion de Bernoulli–Laplace

1996 ◽  
Vol 33 (3) ◽  
pp. 688-697
Author(s):  
Djaouad Taïbi
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Asymptotic Approximation ◽  
Legendre Polynomials ◽  
Transition Density ◽  
Second Stage ◽  
Classical Scheme ◽  
The Mean ◽  
Laplace Diffusion

A generalization of the Bernoulli–Laplace diffusion model is proposed. We consider the case where the number of balls exchanged is greater than one. We show that the stationary distribution is the same as in the classical scheme and we give the mean and the variance of the process. In a second stage, we study the asymptotic approximation based on the diffusion process. A solution of transition density is given using Legendre polynomials.

Une généralisation du modèle de diffusion de Bernoulli–Laplace

1996 ◽  
Vol 33 (03) ◽  
pp. 688-697
Author(s):  
Djaouad Taïbi
Keyword(s):  
Diffusion Process ◽  
Diffusion Model ◽  
Stationary Distribution ◽  
Asymptotic Approximation ◽  
Legendre Polynomials ◽  
Transition Density ◽  
Second Stage ◽  
Classical Scheme ◽  
The Mean ◽  
Laplace Diffusion

A generalization of the Bernoulli–Laplace diffusion model is proposed. We consider the case where the number of balls exchanged is greater than one. We show that the stationary distribution is the same as in the classical scheme and we give the mean and the variance of the process. In a second stage, we study the asymptotic approximation based on the diffusion process. A solution of transition density is given using Legendre polynomials.

scholarly journals A Weak Limit Theorem for Generalized Jiřina Processes

2009 ◽  
Vol 46 (2) ◽  
pp. 453-462 ◽  
Author(s):  
Yuqiang Li
Keyword(s):  
Limit Theorem ◽  
Diffusion Process ◽  
Nonlinear Diffusion ◽  
Weak Limit ◽  
Weak Limit Theorem ◽  
Lévy Jumps

In this paper we prove that a sequence of scaled generalized Jiřina processes can converge weakly to a nonlinear diffusion process with Lévy jumps under certain conditions.

scholarly journals Experimental and Numerical Study on a Grouting Diffusion Model of a Single Rough Fracture in Rock Mass

2020 ◽  
Vol 10 (20) ◽  
pp. 7041
Author(s):  
Wenqi Ding ◽  
Chao Duan ◽  
Qingzhao Zhang
Keyword(s):  
Rock Mass ◽  
Diffusion Process ◽  
Diffusion Model ◽  
Numerical Study ◽  
Structural Characteristics ◽  
Analytical Formula ◽  
Diffusion Experiment ◽  
Cement Slurry ◽  
Temporal And Spatial Distribution ◽  
Rough Fracture

Grouting reinforcement is an important method used to solve problems encountered during tunnel construction, such as collapse and water gushing. The grouting diffusion process is greatly influenced by the structural characteristics of the fractures in a rock mass. First, an analytical grouting diffusion model of a single rough fracture under constant-pressure control is established based on the constitutive equation of a Bingham fluid. Second, the “quasi-elliptical” grouting diffusion pattern under the influence of roughness is revealed through a grouting diffusion experiment, which is conducted with an independently developed visualized testing apparatus. Furthermore, the analytical formula of roughness-corrected grouting diffusion characterized by the saw tooth density is established. Finally, an elaborate numerical simulation of the diffusion process of cement slurry (Bingham flow type) in a single rough fracture is carried out by introducing the Bingham–Papanastasiou rheological model. The temporal and spatial distribution characteristics of the velocity field and pressure field during the grouting diffusion process are analyzed as well. Moreover, the method and range of the roughness correction factor in the analytical grouting diffusion model are proposed based on the fracture roughness unit.

A limit theorem for certain disordered random systems

1994 ◽  
Vol 26 (04) ◽  
pp. 1022-1043 ◽  
Author(s):  
Xinhong Ding
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Limit Theorem ◽  
Random Systems ◽  
Joint Probability ◽  
Dynamical Behaviour ◽  
One Dimensional ◽  
Linear Stochastic Differential Equation ◽  
The One ◽  
Image Position

Many disordered random systems in applications can be described by N randomly coupled Ito stochastic differential equations in : where is a sequence of independent copies of the one-dimensional Brownian motion W and ( is a sequence of independent copies of the ℝ p -valued random vector ξ. We show that under suitable conditions on the functions b, σ, K and Φ the dynamical behaviour of this system in the N → (limit can be described by the non-linear stochastic differential equation where P(t, dx dy) is the joint probability law of ξ and X(t).

scholarly journals Operators with a Single Spectrum

1966 ◽  
Vol 15 (1) ◽  
pp. 11-18 ◽  
Author(s):  
T. T. West
Keyword(s):  
Linear Space ◽  
Normed Linear Space ◽  
Linear Operators ◽  
Complex Field ◽  
Unique Extension ◽  
Single Spectrum ◽  
Bounded Linear ◽  
Infinite Dimensional ◽  
Resolvent Set ◽  
Image Position

Let X be an infinite dimensional normed linear space over the complex field Z. X will not be complete, in general, and its completion will be denoted by . If ℬ(X) is the algebra of all bounded linear operators in X then T ∈ ℬ(X) has a unique extension and . The resolvent set of T ∈ ℬ(X) is defined to beand the spectrum of T is the complement of ρ(T) in Z.

scholarly journals Maximal Subgroups and Irreducible Representations of Generalized Multi-Edge Spinal Groups

2018 ◽  
Vol 61 (3) ◽  
pp. 673-703 ◽  
Author(s):  
Benjamin Klopsch ◽  
Anitha Thillaisundaram
Keyword(s):  
Rooted Tree ◽  
Maximal Subgroups ◽  
Irreducible Representations ◽  
Prime Field ◽  
Infinite Dimensional ◽  
Special Cases ◽  
Profinite Completions ◽  
Spinal Group ◽  
Groups Acting On Trees ◽  
Image Position

AbstractLet p ≥ 3 be a prime. A generalized multi-edge spinal group $$G = \langle \{ a\} \cup \{ b_i^{(j)} {\rm \mid }1 \le j \le p,\, 1 \le i \le r_j\} \rangle \le {\rm Aut}(T)$$ is a subgroup of the automorphism group of a regular p-adic rooted tree T that is generated by one rooted automorphism a and p families $b^{(j)}_{1}, \ldots, b^{(j)}_{r_{j}}$ of directed automorphisms, each family sharing a common directed path disjoint from the paths of the other families. This notion generalizes the concepts of multi-edge spinal groups, including the widely studied GGS groups (named after Grigorchuk, Gupta and Sidki), and extended Gupta–Sidki groups that were introduced by Pervova [‘Profinite completions of some groups acting on trees, J. Algebra310 (2007), 858–879’]. Extending techniques that were developed in these more special cases, we prove: generalized multi-edge spinal groups that are torsion have no maximal subgroups of infinite index. Furthermore, we use tree enveloping algebras, which were introduced by Sidki [‘A primitive ring associated to a Burnside 3-group, J. London Math. Soc.55 (1997), 55–64’] and Bartholdi [‘Branch rings, thinned rings, tree enveloping rings, Israel J. Math.154 (2006), 93–139’], to show that certain generalized multi-edge spinal groups admit faithful infinite-dimensional irreducible representations over the prime field ℤ/pℤ.

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