scholarly journals An application of the KMT construction to the pathwise weak error in the Euler approximation of one-dimensional diffusion process with linear diffusion coefficient

2017 ◽  
Vol 27 (4) ◽  
pp. 2419-2454
Author(s):  
Emmanuelle Clément ◽  
Arnaud Gloter
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Process ◽  
Linear Diffusion ◽  
Euler Approximation ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Weak Error

scholarly journals Role of Time Relaxation in a One-Dimensional Diffusion-Advection Model of Water and Salt Transport

2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Igor Medved’ ◽  
Robert Černý
Keyword(s):  
Diffusion Coefficient ◽  
Structural Damage ◽  
Building Materials ◽  
Chloride Transport ◽  
Salt Transport ◽  
One Dimensional ◽  
Advection Diffusion ◽  
Dimensional Diffusion ◽  
Lime Plaster

The transport of salt, necessarily coupled with the transport of water, through porous building materials may heavily limit their durability due to possible deterioration and structural damage. Usually, the binding of salt to the pore walls is assumed to occur instantly, as soon as the salt is transported by water to a given position. We consider the advection-diffusion model of the transport and generalize it to include possible delays in the binding. Applying the Boltzmann-Matano method, we calculate the diffusion coefficient of the salt in dependence on the salt concentration and show that it increases with the rate of binding. We apply our results to an example of the chloride transport in a lime plaster.

scholarly journals LQG Homing in a Finite Time Interval

2011 ◽  
Vol 2011 ◽  
pp. 1-3 ◽  
Author(s):  
Mario Lefebvre
Keyword(s):  
Optimal Control ◽  
Diffusion Process ◽  
First Passage Time ◽  
Passage Time ◽  
Time Interval ◽  
Finite Time Interval ◽  
First Passage ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Fixed Constant

LetX(t)be a controlled one-dimensional diffusion process having constant infinitesimal variance. We consider the problem of optimally controllingX(t)until timeT(x)=min{T1(x),t1}, whereT1(x)is the first-passage time of the process to a given boundary andt1is a fixed constant. The optimal control is obtained explicitly in the particular case whenX(t)is a controlled Wiener process.

Co-dimension Two Bifurcations in the Presence of Noise

1991 ◽  
Vol 58 (1) ◽  
pp. 259-265 ◽  
Author(s):  
N. Sri Namachchivaya
Keyword(s):  
Normal Form ◽  
Diffusion Process ◽  
Stochastic Averaging ◽  
Singularly Perturbed ◽  
Stability Conditions ◽  
Exit Times ◽  
Double Zero ◽  
One Dimensional ◽  
Dimensional Diffusion ◽  
Stochastic Bifurcations

Some results pertaining to co-dimension two stochastic bifurcations are presented. The normal form associated with non-semi-simple double-zero eigenvalues is considered. The method of stochastic averaging applicable for singularly perturbed stochastic differential equations is used to further reduce the problem to a one dimensional diffusion process. Probability density, most probable values, stability conditions in probability, and mean exit times are obtained for the reduced system.

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