scholarly journals A Random Interval Filling Problem

1962 ◽  
Vol 33 (2) ◽  
pp. 702-718 ◽  
Author(s):  
P. E. Ney
Keyword(s):  
Random Interval ◽  
Interval Filling ◽  
Filling Problem

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (02) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx , the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

A one dimensional random space-filling problem

1968 ◽  
Vol 5 (2) ◽  
pp. 427-435 ◽  
Author(s):  
John P. Mullooly
Keyword(s):  
Asymptotic Behavior ◽  
Finite Number ◽  
Real Line ◽  
Random Variables ◽  
Random Interval ◽  
Space Filling ◽  
One Dimensional ◽  
The Real ◽  
Fixed Constant ◽  
Filling Problem

Consider an interval of the real line (0, x), x > 0; and place in it a random subinterval S(x) defined by the random variables Xx and Yx, the position of the center of S(x) and the length of S(x). The set (0, x)– S(x) consists of two intervals of length δ and η. Let a > 0 be a fixed constant. If δ ≦ a, then a random interval S(δ) defined by Xδ, Yδ is placed in the interval of length δ. If δ < a, the placement of the second interval is not made. The same is done for the interval of length η. Continue to place non-intersecting random subintervals in (0, x), and require that the lengths of all the random subintervals be ≦ a. The process terminates after a finite number of steps when all the segments of (0, x) uncovered by random subintervals are of length < a. At this stage, we say that (0, x) is saturated. Define N(a, x) as the number of random subintervals that have been placed when the process terminates. We are interested in the asymptotic behavior of the moments of N(a, x), for large x.

scholarly journals Representations of hermite processes using local time of intersecting stationary stable regenerative sets

2020 ◽  
Vol 57 (4) ◽  
pp. 1234-1251
Author(s):  
Shuyang Bai
Keyword(s):  
Long Range ◽  
Local Time ◽  
Limit Theorems ◽  
Local Times ◽  
Long Range Dependence ◽  
Random Interval ◽  
Stationary Increments ◽  
Self Similar ◽  
Regenerative Sets

AbstractHermite processes are a class of self-similar processes with stationary increments. They often arise in limit theorems under long-range dependence. We derive new representations of Hermite processes with multiple Wiener–Itô integrals, whose integrands involve the local time of intersecting stationary stable regenerative sets. The proof relies on an approximation of regenerative sets and local times based on a scheme of random interval covering.

The Filling Problem in the Cube

2015 ◽  
Vol 55 (2) ◽  
pp. 249-262
Author(s):  
Dominic Dotterrer
Keyword(s):  
Filling Problem

The law of the Iterated Logarithm for random interval homeomorphisms

2021 ◽  
Author(s):  
Klaudiusz Czudek ◽  
Tomasz Szarek ◽  
Hanna Wojewódka-Ściążko
Keyword(s):  
Random Interval ◽  
Iterated Logarithm ◽  
The Law

Response-Reinforcer Relationships in Variable Delay and Non-Contingent Schedules of Reinforcement

1973 ◽  
Vol 33 (2) ◽  
pp. 627-631 ◽  
Author(s):  
Gerald D. Lachter
Keyword(s):  
Multiple Schedule ◽  
Pause Duration ◽  
Interval Schedule ◽  
Variable Delay ◽  
Random Interval ◽  
Schedules Of Reinforcement ◽  
Schedule Of Reinforcement ◽  
Delay Component

Following 30 sessions of training on a 60-sec. random-interval schedule of reinforcement, 2 pigeons were exposed to a multiple schedule containing non-contingent and variable delay components that provided equal frequencies of reinforcement. The introduction of the multiple schedule resulted in decreased response rare in both components, with a higher rate maintained under the variable delay. Post-reinforcement pauses were systematically increased during the non-contingent schedule, but no systematic increases in pause duration were noted for the variable delay component.

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