Loading [MathJax]/extensions/MathZoom.js
We give a sufficient condition for a non-negative random variable to be of Pareto type by investigating the Laplace-Stieltjes transform of the cumulative distribution function. We focus on the relation between the singularity at the real point of the axis of convergence and the asymptotic decay of the tail probability. For the proof of our theorems, we apply Graham-Vaaler’s complex Tauberian theorem. As an application of our theorems, we consider the asymptotic decay of the stationary distribution...
In this paper, we face a generalization of
the problem of finding the distribution of how long
it takes to reach a “target” set T of states in
Markov chain. The graph problems of finding the number of paths that
go from a state to a target set and of finding the n-length path connections
are shown to belong to this generalization.
This paper explores how the state
space of the Markov chain can be reduced by collapsing together
those states that behave in the same way for the purposes of
calculating...
We add sequential operations to the categorical algebra of weighted and Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters,
arXiv:0909.4136]. The extra expressiveness of the algebra permits the description of hierarchical systems, and ones with evolving geometry. We make a comparison with the probabilistic automata of Lynch et al. [SIAM J. Comput. 37 (2007) 977–1013].
We add sequential operations to the categorical algebra of weighted and
Markov automata introduced in [L. de Francesco Albasini, N. Sabadini and R.F.C. Walters,
arXiv:0909.4136]. The extra
expressiveness of
the algebra permits the description of hierarchical systems, and ones with
evolving geometry. We make a comparison with the probabilistic automata of
Lynch et al. [SIAM J. Comput.37 (2007) 977–1013].
Consider an Hermitean matrix valued stochastic process where the elements evolve according to Ornstein-Uhlenbeck processes. It is well known that the eigenvalues perform a so called Dyson Brownian motion, that is they behave as Ornstein-Uhlenbeck processes conditioned never to intersect.In this paper we study not only the eigenvalues of the full matrix, but also the eigenvalues of all the principal minors. That is, the eigenvalues of the minors in the upper left corner of . Projecting this...
We study the exit path from a general domain after the last visit
to a set of a Markov chain with rare transitions. We prove several
large deviation principles for the law of the succession of the
cycles visited by the process (the cycle path), the succession of
the saddle points gone through to jump from cycle to cycle on the
cycle path (the saddle path) and the succession of all the points
gone through (the exit path). We estimate the time the process
spends in each cycle of the cycle path...
Parallel multi-deme genetic algorithms are especially advantageous because they allow reducing the time of computations and can perform a much broader search than single-population ones. However, their formal analysis does not seem to have been studied exhaustively enough. In this paper we propose a mathematical framework describing a wide class of island-like strategies as a stationary Markov chain. Our approach uses extensively the modeling principles introduced by Vose, Rudolph and their collaborators....
The logarithmic Sobolev constant is always bounded above by half the spectral gap. It is natural to ask when this inequality is an equality. We consider this question in the context of reversible Markov chains on small finite state spaces. In particular, we prove that equality holds for simple random walk on the five cycle and we discuss assorted families of chains on three and four points.
Currently displaying 1 –
20 of
34