A Functional Limit Theorem for the Integrals over Level Sets of a Gaussian Random Field

2016 ◽  
Vol 60 (1) ◽  
pp. 150-161
Author(s):  
A. Shashkin
Keyword(s):  
Limit Theorem ◽  
Random Field ◽  
Level Sets ◽  
Gaussian Random Field ◽  
Functional Limit Theorem ◽  
Functional Limit

scholarly journals The Transparent Dead Leaves Model

2012 ◽  
Vol 44 (01) ◽  
pp. 1-20 ◽  
Author(s):  
B. Galerne ◽  
Y. Gousseau
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Random Field ◽  
Central Limit ◽  
Gaussian Random Field ◽  
Natural Images ◽  
Simulation Algorithm ◽  
New Model ◽  
Grain Model ◽  
Dead Leaves Model

In this paper we introduce the transparent dead leaves (TDL) random field, a new germ-grain model in which the grains are combined according to a transparency principle. Informally, this model may be seen as the superposition of infinitely many semitransparent objects. It is therefore of interest in view of the modeling of natural images. Properties of this new model are established and a simulation algorithm is proposed. The main contribution of the paper is to establish a central limit theorem, showing that, when varying the transparency of the grain from opacity to total transparency, the TDL model ranges from the dead leaves model to a Gaussian random field.

Convergence to the local time of Brownian meander

2019 ◽  
Vol 29 (3) ◽  
pp. 149-158 ◽  
Author(s):  
Valeriy. I. Afanasyev
Keyword(s):  
Random Walk ◽  
Limit Theorem ◽  
Local Time ◽  
Random Processes ◽  
Functional Limit Theorem ◽  
Zero Drift ◽  
Functional Limit ◽  
Brownian Meander

Abstract Let {Sn, n ≥ 0} be integer-valued random walk with zero drift and variance σ2. Let ξ(k, n) be number of t ∈ {1, …, n} such that S(t) = k. For the sequence of random processes $\begin{array}{} \xi(\lfloor u\sigma \sqrt{n}\rfloor,n) \end{array}$ considered under conditions S1 > 0, …, Sn > 0 a functional limit theorem on the convergence to the local time of Brownian meander is proved.

A conditioned functional limit theorem

1980 ◽  
Vol 12 (2) ◽  
pp. 296-297
Author(s):  
Wim Vervaat ◽  
J. C. Smit
Keyword(s):  
Limit Theorem ◽  
Functional Limit Theorem ◽  
Functional Limit
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