61,750 research outputs found
Accuracy of simulations for stochastic dynamic models
This paper provides a general framework for the simulation of stochastic dynamic models. Our analysis rests upon a continuity property of invariant distributions and a generalized law of large numbers. We then establish that the simulated moments from numerical approximations converge to their exact values as the approximation errors of the computed solutions converge to zero. These asymptotic results are of further interest in the comparative study of dynamic solutions, model estimation, and derivation of error bounds for the simulated moments
A perturbation analysis of some Markov chains models with time-varying parameters
We study some regularity properties in locally stationary Markov models which
are fundamental for controlling the bias of nonparametric kernel estimators. In
particular, we provide an alternative to the standard notion of derivative
process developed in the literature and that can be used for studying a wide
class of Markov processes. To this end, for some families of V-geometrically
ergodic Markov kernels indexed by a real parameter u, we give conditions under
which the invariant probability distribution is differentiable with respect to
u, in the sense of signed measures. Our results also complete the existing
literature for the perturbation analysis of Markov chains, in particular when
exponential moments are not finite. Our conditions are checked on several
original examples of locally stationary processes such as integer-valued
autoregressive processes, categorical time series or threshold autoregressive
processes
Statistics of transitions for Markov chains with periodic forcing
The influence of a time-periodic forcing on stochastic processes can
essentially be emphasized in the large time behaviour of their paths. The
statistics of transition in a simple Markov chain model permits to quantify
this influence. In particular the first Floquet multiplier of the associated
generating function can be explicitly computed and related to the equilibrium
probability measure of an associated process in higher dimension. An
application to the stochastic resonance is presented.Comment: 21 page
Schur dynamics of the Schur processes
We construct discrete time Markov chains that preserve the class of Schur
processes on partitions and signatures.
One application is a simple exact sampling algorithm for
q^{volume}-distributed skew plane partitions with an arbitrary back wall.
Another application is a construction of Markov chains on infinite
Gelfand-Tsetlin schemes that represent deterministic flows on the space of
extreme characters of the infinite-dimensional unitary group.Comment: 22 page
Invariant Measures for Hybrid Stochastic Systems
In this paper, we seek to understand the behavior of dynamical systems that
are perturbed by a parameter that changes discretely in time. If we impose
certain conditions, we can study certain embedded systems within a hybrid
system as time-homogeneous Markov processes. In particular, we prove the
existence of invariant measures for each embedded system and relate the
invariant measures for the various systems through the flow. We calculate these
invariant measures explicitly in several illustrative examples.Comment: 18 pages, 7 figure
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