6,292 research outputs found
Dynamical fluctuations for semi-Markov processes
We develop an Onsager-Machlup-type theory for nonequilibrium semi-Markov
processes. Our main result is an exact large time asymptotics for the joint
probability of the occupation times and the currents in the system,
establishing some generic large deviation structures. We discuss in detail how
the nonequilibrium driving and the non-exponential waiting time distribution
influence the occupation-current statistics. The violation of the Markov
condition is reflected in the emergence of a new type of nonlocality in the
fluctuations. Explicit solutions are obtained for some examples of driven
random walks on the ring.Comment: Minor changes, accepted for publication in Journal of Physics
Affinity and Fluctuations in a Mesoscopic Noria
We exhibit the invariance of cycle affinities in finite state Markov
processes under various natural probabilistic constructions, for instance under
conditioning and under a new combinatorial construction that we call ``drag and
drop''. We show that cycle affinities have a natural probabilistic meaning
related to first passage non-equilibrium fluctuation relations that we
establish.Comment: 30 pages, 1 figur
Continuous Equilibrium in Affine and Information-Based Capital Asset Pricing Models
We consider a class of generalized capital asset pricing models in continuous
time with a finite number of agents and tradable securities. The securities may
not be sufficient to span all sources of uncertainty. If the agents have
exponential utility functions and the individual endowments are spanned by the
securities, an equilibrium exists and the agents' optimal trading strategies
are constant. Affine processes, and the theory of information-based asset
pricing are used to model the endogenous asset price dynamics and the terminal
payoff. The derived semi-explicit pricing formulae are applied to numerically
analyze the impact of the agents' risk aversion on the implied volatility of
simultaneously-traded European-style options.Comment: 24 pages, 4 figure
Current fluctuations in stochastic systems with long-range memory
We propose a method to calculate the large deviations of current fluctuations
in a class of stochastic particle systems with history-dependent rates.
Long-range temporal correlations are seen to alter the speed of the large
deviation function in analogy with long-range spatial correlations in
equilibrium systems. We give some illuminating examples and discuss the
applicability of the Gallavotti-Cohen fluctuation theorem.Comment: 10 pages, 1 figure. v2: Minor alterations. v3: Very minor alterations
for consistency with published version appearing at
http://stacks.iop.org/1751-8121/42/34200
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