Applications and Limitations of Perfect Simulation

2016 ◽  
pp. 221-240
Keyword(s):  
Perfect Simulation

Perfect Simulation for Image Restoration

2007 ◽  
Vol 23 (3) ◽  
pp. 475-487
Author(s):  
Mark Huber
Keyword(s):  
Image Restoration ◽  
Perfect Simulation

scholarly journals Chains with unbounded variable length memory: perfect simulation and a visible regeneration scheme

2011 ◽  
Vol 43 (03) ◽  
pp. 735-759 ◽  
Author(s):  
Sandro Gallo
Keyword(s):  
Transition Probabilities ◽  
Natural Extension ◽  
Continuity Condition ◽  
Variable Length ◽  
Perfect Simulation ◽  
Simulation Algorithm ◽  
Deterministic Function ◽  
The Family ◽  
Context Tree ◽  
Probabilistic Context

We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infinite memory chains for which the family of transition probabilities is represented by a probabilistic context tree. We do not assume any continuity condition: our condition is expressed in terms of the structure of the context tree. More precisely, the length of the contexts is a deterministic function of the distance to the last occurrence of some determined string of symbols. It turns out that the resulting class of chains can be seen as a natural extension of the class of chains having a renewal string. In particular, our chains exhibit a visible regeneration scheme.

scholarly journals Exact Monte Carlo simulation for fork-join networks

2011 ◽  
Vol 43 (02) ◽  
pp. 484-503 ◽  
Author(s):  
Hongsheng Dai
Keyword(s):  
Monte Carlo ◽  
Response Times ◽  
Simulation Method ◽  
Perfect Simulation ◽  
Analytic Approximations ◽  
The Past ◽  
Coupling From The Past ◽  
Service Stations ◽  
Explicit Formulae ◽  
Queue Lengths

In a fork-join network each incoming job is split into K tasks and the K tasks are simultaneously assigned to K parallel service stations for processing. For the distributions of response times and queue lengths of fork-join networks, no explicit formulae are available. Existing methods provide only analytic approximations for the response time and the queue length distributions. The accuracy of such approximations may be difficult to justify for some complicated fork-join networks. In this paper we propose a perfect simulation method based on coupling from the past to generate exact realisations from the equilibrium of fork-join networks. Using the simulated realisations, Monte Carlo estimates for the distributions of response times and queue lengths of fork-join networks are obtained. Comparisons of Monte Carlo estimates and theoretical approximations are also provided. The efficiency of the sampling algorithm is shown theoretically and via simulation.

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