Non-Markovian Processes

2017 ◽  
pp. 252-271
Keyword(s):  
Markovian Processes

scholarly journals Phenomenological memory-kernel master equations and time-dependent Markovian processes

2010 ◽  
Vol 81 (6) ◽  
Author(s):  
L. Mazzola ◽  
E.-M. Laine ◽  
H.-P. Breuer ◽  
S. Maniscalco ◽  
J. Piilo
Keyword(s):  
Master Equations ◽  
Time Dependent ◽  
Memory Kernel ◽  
Markovian Processes

Characterizing Fractal and Hierarchical Morphologies Beyond the Fractal Dimension

1994 ◽  
Vol 367 ◽  
Author(s):  
Raphael Blumenfeld ◽  
Robin C. Ball
Keyword(s):  
Asymptotic Behavior ◽  
Fractal Dimension ◽  
Finite Size ◽  
Size Analysis ◽  
Corrections To Scaling ◽  
Diffusion Limited Aggregation ◽  
Diffusion Limited ◽  
Markovian Processes ◽  
Branching Patterns ◽  
Admissible Solutions

AbstractWe present a novel correlation scheme to characterize the morphology of fractal and hierarchical patterns beyond traditional scaling. The method consists of analysing correlations between more than two-points in logarithmic coordinates. This technique has several advantages: i) It can be used to quantify the currently vague concept of morphology; ii) It allows to distinguish between different signatures of structures with similar fractal dimension but different morphologies already for relatively small systems; iii) The method is sensitive to oscillations in logarithmic coordinates, which are both admissible solutions for renormalization equations and which appear in many branching patterns (e.g., noise-reduced diffusion-limited-aggregation and bronchial structures); iv) The methods yields information on corrections to scaling from the asymptotic behavior, which is very useful in finite size analysis. Markovian processes are calculated exactly and several structures are analyzed by this method to demonstrate its advantages.

scholarly journals On the optimal importance process for piecewise deterministic Markov process

2019 ◽  
Vol 23 ◽  
pp. 893-921
Author(s):  
H. Chraibi ◽  
A. Dutfoy ◽  
T. Galtier ◽  
J. Garnier
Keyword(s):  
Importance Sampling ◽  
Simulation Study ◽  
Variance Reduction ◽  
Sampling Method ◽  
Piecewise Deterministic Markov Process ◽  
Importance Sampling Method ◽  
Markovian Processes ◽  
Component Systems ◽  
Reference Measure ◽  
Reduction Methods

In order to assess the reliability of a complex industrial system by simulation, and in reasonable time, variance reduction methods such as importance sampling can be used. We propose an adaptation of this method for a class of multi-component dynamical systems which are modeled by piecewise deterministic Markovian processes (PDMP). We show how to adapt the importance sampling method to PDMP, by introducing a reference measure on the trajectory space. This reference measure makes it possible to identify the admissible importance processes. Then we derive the characteristics of an optimal importance process, and present a convenient and explicit way to build an importance process based on theses characteristics. A simulation study compares our importance sampling method to the crude Monte-Carlo method on a three-component systems. The variance reduction obtained in the simulation study is quite spectacular.

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