166 research outputs found
The exit problem for diffusions with time-periodic drift and stochastic resonance
Physical notions of stochastic resonance for potential diffusions in
periodically changing double-well potentials such as the spectral power
amplification have proved to be defective. They are not robust for the passage
to their effective dynamics: continuous-time finite-state Markov chains
describing the rough features of transitions between different domains of
attraction of metastable points. In the framework of one-dimensional diffusions
moving in periodically changing double-well potentials we design a new notion
of stochastic resonance which refines Freidlin's concept of quasi-periodic
motion. It is based on exact exponential rates for the transition probabilities
between the domains of attraction which are robust with respect to the reduced
Markov chains. The quality of periodic tuning is measured by the probability
for transition during fixed time windows depending on a time scale parameter.
Maximizing it in this parameter produces the stochastic resonance points.Comment: Published at http://dx.doi.org/10.1214/105051604000000530 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Existence, Uniqueness and Regularity of Decoupling Fields to Multidimensional Fully Coupled FBSDEs
We develop an existence, uniqueness and regularity theory for general
multidimensional strongly coupled FBSDE using so called decoupling fields. We
begin with a local result and extend it to a global theory via concatenation.
The cornerstone of the global theory is the so called maximal interval which
is, roughly speaking, the largest interval on which reasonable solutions exist.
A method to verify that the maximal interval is the whole interval, for
problems in which this is conjectured, is proposed. As part of our study of the
regularity of solutions constructed we show variational differentiability under
Lipschitz assumptions. Extra emphasis is put on the more special Markovian case
in which assumptions on the Lipschitz continuity for the FBSDE can be weakened
to local ones, and additional regularity properties emerge
A two state model for noise-induced resonance in bistable systems with delay
The subject of the present paper is a simplified model for a symmetric bistable system with memory or delay, the reference model, which in the presence of noise exhibits a phenomenon similar to what is known as stochastic resonance. The reference model is given by a one dimensional parametrized stochastic differential equation with point delay, basic properties whereof we check. With a view to capturing the effective dynamics and, in particular, the resonance-like behaviour of the reference model we construct a simplified or reduced model, the two state model, first in discrete time, then in the limit of discrete time tending to continuous time. The main advantage of the reduced model is that it enables us to explicitly calculate the distribution of residence times which in turn can be used to characterize the phenomenon of noise-induced resonance. Drawing on what has been proposed in the physics literature, we outline a heuristic method for establishing the link between the two state model and the reference model. The resonance characteristics developed for the reduced model can thus be applied to the original model.logit model, utility maximization nested logit, non-normalized nested logit, simulation study
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