scholarly journals A note on the exact simulation of spherical Brownian motion

2020 ◽  
Vol 165 ◽  
pp. 108836
Author(s):  
Aleksandar Mijatović ◽  
Veno Mramor ◽  
Gerónimo Uribe Bravo
Keyword(s):  
Brownian Motion ◽  
Exact Simulation

scholarly journals Exact Simulation for Diffusion Bridges: An Adaptive Approach

2014 ◽  
Vol 51 (02) ◽  
pp. 346-358
Author(s):  
Hongsheng Dai
Keyword(s):  
Brownian Motion ◽  
Sampling Methods ◽  
Simulation Method ◽  
New Method ◽  
Sampling Techniques ◽  
Rejection Sampling ◽  
Exact Simulation ◽  
Adaptive Approach

Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation.

scholarly journals Exact simulation of multidimensional reflected Brownian motion

2018 ◽  
Vol 55 (1) ◽  
pp. 137-156
Author(s):  
Jose Blanchet ◽  
Karthyek Murthy
Keyword(s):  
Brownian Motion ◽  
Information Structure ◽  
Piecewise Linear ◽  
Simulation Method ◽  
Uniform Norm ◽  
Piecewise Linear Approximation ◽  
Reflected Brownian Motion ◽  
Proposal Distribution ◽  
Exact Simulation ◽  
Simulation Techniques

AbstractWe present the first exact simulation method for multidimensional reflected Brownian motion (RBM). Exact simulation in this setting is challenging because of the presence of correlated local-time-like terms in the definition of RBM. We apply recently developed so-called ε-strong simulation techniques (also known as tolerance-enforced simulation) which allow us to provide a piecewise linear approximation to RBM with ε (deterministic) error in uniform norm. A novel conditional acceptance–rejection step is then used to eliminate the error. In particular, we condition on a suitably designed information structure so that a feasible proposal distribution can be applied.

scholarly journals Exact Simulation for Diffusion Bridges: An Adaptive Approach

2014 ◽  
Vol 51 (2) ◽  
pp. 346-358 ◽  
Author(s):  
Hongsheng Dai
Keyword(s):  
Brownian Motion ◽  
Sampling Methods ◽  
Simulation Method ◽  
New Method ◽  
Sampling Techniques ◽  
Rejection Sampling ◽  
Exact Simulation ◽  
Adaptive Approach

Exact simulation approaches for a class of diffusion bridges have recently been proposed based on rejection sampling techniques. The existing rejection sampling methods may not be practical owing to small acceptance probabilities. In this paper we propose an adaptive approach that improves the existing methods significantly under certain scenarios. The idea of the new method is based on a layered process, which can be simulated from a layered Brownian motion with reweighted layer probabilities. We will show that the new exact simulation method is more efficient than existing methods theoretically and via simulation.

Integrated Fractional white Noise as an Alternative to Multifractional Brownian Motion

2007 ◽  
Vol 44 (02) ◽  
pp. 393-408 ◽  
Author(s):  
Allan Sly
Keyword(s):  
Stochastic Process ◽  
Brownian Motion ◽  
White Noise ◽  
Gaussian Process ◽  
Discrete Data ◽  
Hölder Exponent ◽  
Scaling Properties ◽  
Multifractional Brownian Motion ◽  
Local Properties

Multifractional Brownian motion is a Gaussian process which has changing scaling properties generated by varying the local Hölder exponent. We show that multifractional Brownian motion is very sensitive to changes in the selected Hölder exponent and has extreme changes in magnitude. We suggest an alternative stochastic process, called integrated fractional white noise, which retains the important local properties but avoids the undesirable oscillations in magnitude. We also show how the Hölder exponent can be estimated locally from discrete data in this model.

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