scholarly journals Monte Carlo Filtering of Piecewise Deterministic Processes

2011 ◽  
Vol 20 (1) ◽  
pp. 119-139 ◽  
Author(s):  
Nick Whiteley ◽  
Adam M. Johansen ◽  
Simon Godsill
Keyword(s):  
Monte Carlo ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes

scholarly journals Thinning and multilevel Monte Carlo methods for piecewise deterministic (Markov) processes with an application to a stochastic Morris–Lecar model

2020 ◽  
Vol 52 (1) ◽  
pp. 138-172
Author(s):  
Vincent Lemaire ◽  
MichÉle Thieullen ◽  
Nicolas Thomas
Keyword(s):  
Monte Carlo ◽  
Markov Processes ◽  
Building Blocks ◽  
Not Given ◽  
Multilevel Monte Carlo ◽  
The Third ◽  
Piecewise Deterministic Markov Processes ◽  
Deterministic Processes ◽  
Piecewise Deterministic Processes ◽  
Weak Error

AbstractIn the first part of this paper we study approximations of trajectories of piecewise deterministic processes (PDPs) when the flow is not given explicitly by the thinning method. We also establish a strong error estimate for PDPs as well as a weak error expansion for piecewise deterministic Markov processes (PDMPs). These estimates are the building blocks of the multilevel Monte Carlo (MLMC) method, which we study in the second part. The coupling required by the MLMC is based on the thinning procedure. In the third part we apply these results to a two-dimensional Morris–Lecar model with stochastic ion channels. In the range of our simulations the MLMC estimator outperforms classical Monte Carlo.

Systematically Interrogating Agent-Based Models

2017 ◽  
Author(s):  
Michael Laver ◽  
Ernest Sergenti
Keyword(s):  
Stochastic Process ◽  
Monte Carlo ◽  
Markov Chain ◽  
Experimental Design ◽  
Stochastic Processes ◽  
Agent Based ◽  
Estimation Strategy ◽  
Deterministic Processes ◽  
Time Average ◽  
Single State

This chapter develops the methods for designing, executing, and analyzing large suites of computer simulations that generate stable and replicable results. It starts with a discussion of the different methods of experimental design, such as grid sweeping and Monte Carlo parameterization. Next, it demonstrates how to calculate mean estimates of output variables of interest. It does so by first discussing stochastic processes, Markov Chain representations, and model burn-in. It focuses on three stochastic process representations: nonergodic deterministic processes that converge on a single state; nondeterministic stochastic processes for which a time average provides a representative estimate of the output variables; and nondeterministic stochastic processes for which a time average does not provide a representative estimate of the output variables. The estimation strategy employed depends on which stochastic process the simulation follows. Lastly, the chapter presents a set of diagnostic checks used to establish an appropriate sample size for the estimation of the means.

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