12,022 research outputs found
Universal Nonlinear Filtering Using Feynman Path Integrals II: The Continuous-Continuous Model with Additive Noise
In this paper, the Feynman path integral formulation of the
continuous-continuous filtering problem, a fundamental problem of applied
science, is investigated for the case when the noise in the signal and
measurement model is additive. It is shown that it leads to an independent and
self-contained analysis and solution of the problem. A consequence of this
analysis is Feynman path integral formula for the conditional probability
density that manifests the underlying physics of the problem. A corollary of
the path integral formula is the Yau algorithm that has been shown to be
superior to all other known algorithms. The Feynman path integral formulation
is shown to lead to practical and implementable algorithms. In particular, the
solution of the Yau PDE is reduced to one of function computation and
integration.Comment: Interdisciplinary, 41 pages, 5 figures, JHEP3 class; added more
discussion and reference
The high energy asymptotics of scattering processes in QCD
High energy scattering in the QCD parton model was recently shown to be a
reaction-diffusion process, and thus to lie in the universality class of the
stochastic Fisher-Kolmogorov-Petrovsky-Piscounov equation. We recall that the
latter appears naturally in the context of the parton model. We provide a
thorough numerical analysis of the mean field approximation, given in QCD by
the Balitsky-Kovchegov equation. In the framework of a simple stochastic toy
model that captures the relevant features of QCD, we discuss and illustrate the
universal properties of such stochastic models. We investigate in particular
the validity of the mean field approximation and how it is broken by
fluctuations. We find that the mean field approximation is a good approximation
in the initial stages of the evolution in rapidity.Comment: 31 pages, 20 figures. The code for BK evolution can be downloaded
from http://www.isv.uu.se/~enberg/BK/ v2: several points clarified,
discussion of the solutions to the mean-field evolution enhanced through the
study of a different class of initial conditions, references added;
conclusions unchanged. To appear in Phys. Rev.
The Effects of a Rapidly-Fluctuating Random Environment on Systems of Interacting Species
Some models of interacting species in a random environment are analyzed. Approximate solutions of the stochastic differential or delay-differential equations describing the systems are obtained, on the assumption that the random environment is fluctuating rapidly
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