scholarly journals Weak Convergence of Finite-Dimensional Distributions of the Number of Empty Boxes in the Bernoulli Sieve

2015 ◽  
Vol 59 (1) ◽  
pp. 87-113 ◽  
Author(s):  
A. M. Iksanov ◽  
A. V. Marynych ◽  
V. A. Vatutin
Keyword(s):  
Weak Convergence ◽  
Finite Dimensional

scholarly journals S-Subgradient Projection Methods with S-Subdifferential Functions for Nonconvex Split Feasibility Problems

Symmetry ◽  
2019 ◽  
Vol 11 (12) ◽  
pp. 1517
Author(s):  
Jinzuo Chen ◽  
Mihai Postolache ◽  
Yonghong Yao
Keyword(s):  
Weak Convergence ◽  
Projection Method ◽  
Split Feasibility Problem ◽  
Projection Methods ◽  
Feasibility Problem ◽  
Split Feasibility Problems ◽  
Finite Dimensional ◽  
Subgradient Projection ◽  
Weak Convergence Theorem ◽  
Split Feasibility

In this paper, the original C Q algorithm, the relaxed C Q algorithm, the gradient projection method ( G P M ) algorithm, and the subgradient projection method ( S P M ) algorithm for the convex split feasibility problem are reviewed, and a renewed S P M algorithm with S-subdifferential functions to solve nonconvex split feasibility problems in finite dimensional spaces is suggested. The weak convergence theorem is established.

scholarly journals Weak convergence of random processes with immigration at random times

2020 ◽  
Vol 57 (1) ◽  
pp. 250-265
Author(s):  
Congzao Dong ◽  
Alexander Iksanov
Keyword(s):  
Weak Convergence ◽  
Branching Processes ◽  
Sufficient Conditions ◽  
Random Processes ◽  
Branching Random Walk ◽  
General Point ◽  
Shot Noise Process ◽  
Finite Dimensional ◽  
Strong Resemblance ◽  
Random Times

AbstractBy a random process with immigration at random times we mean a shot noise process with a random response function (response process) in which shots occur at arbitrary random times. Such random processes generalize random processes with immigration at the epochs of a renewal process which were introduced in Iksanov et al. (2017) and bear a strong resemblance to a random characteristic in general branching processes and the counting process in a fixed generation of a branching random walk generated by a general point process. We provide sufficient conditions which ensure weak convergence of finite-dimensional distributions of these processes to certain Gaussian processes. Our main result is specialised to several particular instances of random times and response processes.

scholarly journals On approximations of the point measures associated with the Brownian web by means of the fractional step method and the discretization of the initial interval

2020 ◽  
Vol 72 (9) ◽  
pp. 1179-1194
Author(s):  
A. A. Dorogovtsev ◽  
M. B. Vovchanskii
Keyword(s):  
Weak Convergence ◽  
Explicit Expression ◽  
Wasserstein Distance ◽  
Fractional Step ◽  
Step Method ◽  
Fractional Step Method ◽  
Initial Interval ◽  
Lebesque Measure ◽  
Finite Dimensional ◽  
Point Measure

UDC 519.21 We establish the rate of weak convergence in the fractional step method for the Arratia flow in terms of the Wasserstein distance between the images of the Lebesque measure under the action of the flow. We introduce finite-dimensional densities that describe sequences of collisions in the Arratia flow and derive an explicit expression for them. With the initial interval discretized, we also discuss the convergence of the corresponding approximations of the point measure associated with the Arratia flow in terms of such densities.

Weak Convergence and One-Sample Rank Statistics Under ϕ-mixing*

1975 ◽  
Vol 18 (4) ◽  
pp. 555-565
Author(s):  
K. L. Mehra
Keyword(s):  
Weak Convergence ◽  
Lebesgue Measure ◽  
Probability Space ◽  
Stationary Process ◽  
Mixing Condition ◽  
Absolutely Continuous ◽  
Rank Statistics ◽  
Finite Dimensional ◽  
Strictly Stationary Process

Let {Xi:i=1, 2,…} be a real strictly stationary process (defined on a probability space (Ω, A, P)) which has absolutely continuous finite dimensional distributions (with respect to Lebesgue measure) and satisfies the ϕ-mixing condition: Let and denote the sub-cr-fields generated, respectively, by {Xi:i≤k} and {Xi:i≥k+n}; then, for each k≥1 and n≥l, and together imply.

scholarly journals Weak convergence of the number of vertices at intermediate levels of random recursive trees

2018 ◽  
Vol 55 (4) ◽  
pp. 1131-1142 ◽  
Author(s):  
Alexander Iksanov ◽  
Zakhar Kabluchko
Keyword(s):  
Asymptotic Behavior ◽  
Weak Convergence ◽  
Gaussian Process ◽  
Branching Processes ◽  
One Dimensional ◽  
Recursive Tree ◽  
Finite Dimensional ◽  
Recursive Trees

Abstract Let Xn(k) be the number of vertices at level k in a random recursive tree with n+1 vertices. We are interested in the asymptotic behavior of Xn(k) for intermediate levels k=kn satisfying kn→∞ and kn=o(logn) as n→∞. In particular, we prove weak convergence of finite-dimensional distributions for the process (Xn ([knu]))u>0, properly normalized and centered, as n→∞. The limit is a centered Gaussian process with covariance (u,v)↦(u+v)−1. One-dimensional distributional convergence of Xn(kn), properly normalized and centered, was obtained with the help of analytic tools by Fuchs et al. (2006). In contrast, our proofs, which are probabilistic in nature, exploit a connection of our model with certain Crump–Mode–Jagers branching processes.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

A closer look at the stable completion

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Inverse Limit ◽  
Unit Vector ◽  
Vector Spaces ◽  
Dimensional Vector ◽  
Compact Sets ◽  
Linear Topology ◽  
Topological Embedding ◽  
Definable Set ◽  
Finite Dimensional ◽  
The One

This chapter introduces the concept of stable completion and provides a concrete representation of unit vector Mathematical Double-Struck Capital A superscript n in terms of spaces of semi-lattices, with particular emphasis on the frontier between the definable and the topological categories. It begins by constructing a topological embedding of unit vector Mathematical Double-Struck Capital A superscript n into the inverse limit of a system of spaces of semi-lattices L(Hsubscript d) endowed with the linear topology, where Hsubscript d are finite-dimensional vector spaces. The description is extended to the projective setting. The linear topology is then related to the one induced by the finite level morphism L(Hsubscript d). The chapter also considers the condition that if a definable set in L(Hsubscript d) is an intersection of relatively compact sets, then it is itself relatively compact.

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