scholarly journals Sequential Monte Carlo methods for Bayesian elliptic inverse problems

2015 ◽  
Vol 25 (4) ◽  
pp. 727-737 ◽  
Author(s):  
Alexandros Beskos ◽  
Ajay Jasra ◽  
Ege A. Muzaffer ◽  
Andrew M. Stuart
Keyword(s):  
Monte Carlo ◽  
Inverse Problems ◽  
Monte Carlo Methods ◽  
Sequential Monte Carlo ◽  
Sequential Monte Carlo Methods ◽  
Elliptic Inverse Problems

Sequential Monte Carlo methods for diffusion processes

2009 ◽  
Vol 465 (2112) ◽  
pp. 3709-3727 ◽  
Author(s):  
Ajay Jasra ◽  
Arnaud Doucet
Keyword(s):  
Optimal Control ◽  
Monte Carlo ◽  
Option Pricing ◽  
Monte Carlo Methods ◽  
Sequential Monte Carlo ◽  
Diffusion Processes ◽  
Time Discretization ◽  
Initial Condition ◽  
Sequential Monte Carlo Methods ◽  
Low Dimensional

In this paper, we show how to use sequential Monte Carlo methods to compute expectations of functionals of diffusions at a given time and the gradients of these quantities w.r.t. the initial condition of the process. In some cases, via the exact simulation of the diffusion, there is no time discretization error, otherwise the methods use Euler discretization. We illustrate our approach on both high- and low-dimensional problems from optimal control and establish that our approach substantially outperforms standard Monte Carlo methods typically adopted in the literature. The methods developed here are appropriate for solving a certain class of partial differential equations as well as for option pricing and hedging.

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