First-Passage-Time Kinetic Monte Carlo Simulation of Nucleation and Growth in Electrodeposition

2014 ◽  
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kinetic Monte Carlo ◽  
First Passage Time ◽  
Passage Time ◽  
Nucleation And Growth ◽  
First Passage ◽  
Kinetic Monte Carlo Simulation

scholarly journals Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

2011 ◽  
Vol 48 (3) ◽  
pp. 699-712 ◽  
Author(s):  
Tomoyuki Ichiba ◽  
Constantinos Kardaras
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kernel Smoothing ◽  
Brownian Bridge ◽  
First Passage Time ◽  
Passage Time ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
First Passage ◽  
One Dimensional

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.

scholarly journals Efficient Estimation of One-Dimensional Diffusion First Passage Time Densities via Monte Carlo Simulation

2011 ◽  
Vol 48 (03) ◽  
pp. 699-712
Author(s):  
Tomoyuki Ichiba ◽  
Constantinos Kardaras
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Kernel Smoothing ◽  
Brownian Bridge ◽  
First Passage Time ◽  
Passage Time ◽  
Efficient Estimation ◽  
Cumulative Distribution ◽  
First Passage ◽  
One Dimensional

We propose a method for estimating first passage time densities of one-dimensional diffusions via Monte Carlo simulation. Our approach involves a representation of the first passage time density as the expectation of a functional of the three-dimensional Brownian bridge. As the latter process can be simulated exactly, our method leads to almost unbiased estimators. Furthermore, since the density is estimated directly, a convergence of order 1 / √N, where N is the sample size, is achieved, which is in sharp contrast to the slower nonparametric rates achieved by kernel smoothing of cumulative distribution functions.

Sign in / Sign up

Export Citation Format

Share Document