Stability and Error Analysis for a Second-Order Fast Approximation of the Local and Nonlocal Diffusion Equations on the Real Line

2020 ◽  
Vol 58 (3) ◽  
pp. 1893-1917
Author(s):  
Chunxiong Zheng ◽  
Qiang Du ◽  
Xiang Ma ◽  
Jiwei Zhang
Keyword(s):  
Error Analysis ◽  
Real Line ◽  
Second Order ◽  
Diffusion Equations ◽  
Nonlocal Diffusion ◽  
The Real ◽  
Stability And Error Analysis

Dependent thinning of point processes

1980 ◽  
Vol 17 (04) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Peano arithmetic may not be interpretable in the monadic theory of linear orders

1997 ◽  
Vol 62 (3) ◽  
pp. 848-872 ◽  
Author(s):  
Shmuel Lifsches ◽  
Saharon Shelah
Keyword(s):  
Real Line ◽  
Order Theory ◽  
Peano Arithmetic ◽  
Second Order ◽  
Linear Orders ◽  
The Real ◽  
Monadic Theory

AbstractGurevich and Shelah have shown that Peano Arithmetic cannot be interpreted in the monadic second-order theory of short chains (hence, in the monadic second-order theory of the real line). We will show here that it is consistent that the monadic second-order theory of no chain interprets Peano Arithmetic.

Dependent thinning of point processes

1980 ◽  
Vol 17 (4) ◽  
pp. 987-995 ◽  
Author(s):  
Valerie Isham
Keyword(s):  
Poisson Process ◽  
Point Process ◽  
Real Line ◽  
Point Processes ◽  
Compound Poisson Process ◽  
Second Order ◽  
Binary Variables ◽  
Compound Poisson ◽  
The Real ◽  
Markov Sequence

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.

Numerical Solution of the Nonlocal Diffusion Equation on the Real Line

2017 ◽  
Vol 39 (5) ◽  
pp. A1951-A1968 ◽  
Author(s):  
Chunxiong Zheng ◽  
Jiashun Hu ◽  
Qiang Du ◽  
Jiwei Zhang
Keyword(s):  
Diffusion Equation ◽  
Numerical Solution ◽  
Real Line ◽  
Nonlocal Diffusion ◽  
The Real

scholarly journals The empirical mean position of a branching Lévy process

2020 ◽  
Vol 57 (4) ◽  
pp. 1252-1259
Author(s):  
David Cheek ◽  
Seva Shneer
Keyword(s):  
Limit Theorem ◽  
Real Line ◽  
Lévy Process ◽  
Second Order ◽  
Levy Process ◽  
The Real

AbstractWe consider a supercritical branching Lévy process on the real line. Under mild moment assumptions on the number of offspring and their displacements, we prove a second-order limit theorem on the empirical mean position.

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