Classical Diffusion Limit of One-Dimensional Hydromagnetic Flow

1968 ◽  
Vol 11 (5) ◽  
pp. 1020
Author(s):  
M. Bineau
Keyword(s):  
Diffusion Limit ◽  
Hydromagnetic Flow ◽  
One Dimensional ◽  
Classical Diffusion

One-Dimensional Hydromagnetic Flow With Small Area Variations

1962 ◽  
Vol 29 (4) ◽  
pp. 474-474
Author(s):  
Roy M. Gundersen
Keyword(s):  
Small Area ◽  
Hydromagnetic Flow ◽  
One Dimensional

scholarly journals Limit theorems for the zig-zag process

2017 ◽  
Vol 49 (3) ◽  
pp. 791-825 ◽  
Author(s):  
Joris Bierkens ◽  
Andrew Duncan
Keyword(s):  
Monte Carlo ◽  
Probability Distributions ◽  
Asymptotic Variance ◽  
Mcmc Methods ◽  
Diffusion Limit ◽  
Switching Rate ◽  
One Dimensional ◽  
Piecewise Deterministic Markov Processes ◽  
Reversible Markov Chains ◽  
The One

AbstractMarkov chain Monte Carlo (MCMC) methods provide an essential tool in statistics for sampling from complex probability distributions. While the standard approach to MCMC involves constructing discrete-time reversible Markov chains whose transition kernel is obtained via the Metropolis–Hastings algorithm, there has been recent interest in alternative schemes based on piecewise deterministic Markov processes (PDMPs). One such approach is based on the zig-zag process, introduced in Bierkens and Roberts (2016), which proved to provide a highly scalable sampling scheme for sampling in the big data regime; see Bierkenset al.(2016). In this paper we study the performance of the zig-zag sampler, focusing on the one-dimensional case. In particular, we identify conditions under which a central limit theorem holds and characterise the asymptotic variance. Moreover, we study the influence of the switching rate on the diffusivity of the zig-zag process by identifying a diffusion limit as the switching rate tends to ∞. Based on our results we compare the performance of the zig-zag sampler to existing Monte Carlo methods, both analytically and through simulations.

One-dimensional classical scattering processes and the diffusion limit

1987 ◽  
Vol 19 (01) ◽  
pp. 81-105 ◽  
Author(s):  
Wilfrid S. Kendall ◽  
Mark Westcott
Keyword(s):  
Brownian Motion ◽  
Asymptotic Behaviour ◽  
Diffusion Limit ◽  
One Dimensional ◽  
Skorokhod Embedding

The method of Skorokhod embedding, that is to say of coupling to Brownian motion, is used to establish the asymptotic behaviour of one-dimensional scattering processes.

A free boundary problem arising in some reacting–diffusing system

1991 ◽  
Vol 118 (3-4) ◽  
pp. 355-378 ◽  
Author(s):  
D. Hilhorst ◽  
Y. Nishiura ◽  
M. Mimura
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Finite Dimension ◽  
Reaction Diffusion ◽  
Diffusion Limit ◽  
Well Posedness ◽  
One Dimensional ◽  
A Free Boundary Problem ◽  
Large Diffusion

SynopsisWe prove the well-posedness for a one-dimensional free boundary problem arising from some reaction diffusion system. The interfacial point hits a boundary point in finite time or remains inside for all time. In the large diffusion limit, the system is reduced to ordinary differential equations of finite dimension.

Raman-Nath equation and classical diffusion on one-dimensional random chains

1985 ◽  
Vol 31 (3) ◽  
pp. 1608-1609 ◽  
Author(s):  
G. Dattoli ◽  
J. Gallardo
Keyword(s):  
One Dimensional ◽  
Classical Diffusion
Sign in / Sign up

Export Citation Format

Share Document