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Among the rich collection of noise sources that can be used to drive stochastic differential equations (SDE), we here focus on Markov processes that themselves are functions of the standard Brownian motion and of the Telegrapher’s process. Our present nois ...
We study some linear and nonlinear shot noise models where the jumps are drawn from a compound Poisson process with jump sizes following an Erlang-m distribution. We show that the associated Master equation can be written as a spatial mth order partial dif ...
The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from (a) a finite extension of the age ...
Although well established in the aviation community, low-cost and vehicle independent "black-box" technology for accident analysis, adapted to mass-market ground-based vehicles, is an emerging technology with growing importance. Whilst several produits sui ...
2013
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We analytically discuss a multiplicative noise generalization of the Kuramoto- Sakaguchi dynamics for an assembly of globally coupled phase oscillators. In the mean-field limit, the resulting class of invariant measures coincides with a generalized, two-par ...
2010
The purpose of this thesis is to show on explicit examples how various theoretical concepts, ranging from statistical mechanics to stochastic control and from traffic theory to queuing systems, can be transferred to transport processes, encountered in part ...
EPFL2005
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The population dynamics of an assembly of globally coupled homogeneous phase oscillators is studied in presence of non-Gaussian fluctuations. The variance of the underlying stochastic process grows as t + \beta^2 t^2 ( \beta being a constant) and therefore ...
