This paper addresses the H2 and H∞ filtering design problems of discrete-time Markov jump linear systems. First, under the assumption that the Markov parameter is measured, the main contribution is on the LMI characterization of all filters such that the estimation error remains bounded by a given norm level, yielding the complete solution of the mode-dependent filtering design problem. Based o...

We study the classical problem of noisy constrained capacity in the case of the binary symmetric channel (BSC), namely, the capacity of a BSC whose inputs are sequences chosen from a constrained set. Motivated by a result of Ordentlich and Weissman [In Proceedings of IEEE Information Theory Workshop (2004) 117–122], we derive an asymptotic formula (when the noise parameter is small) for the ent...

Markov chain Monte Carlo (MCMC) methods use computer simulation of Markov chains in the parameter space. The Markov chains are defined in such a way that the posterior distribution in the given statistical inference problem is the asymptotic distribution. This allows to use ergodic averages to approximate the desired posterior expectations. Several standard approaches to define such Markov chai...

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned Büchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT...

It is shown that the stochastic model of Fényes and Nelson can be generalized in such a way that the diffusion constant of the Markov theory becomes a free parameter. This extra freedom allows one to identify quantum mechanics with a class of Markov processes with diffusion constants varying from 0 to ∞.

Hidden Markov models (HMMs) have become a standard tool for pattern recognition in computer vision. However, issues of parameter estimation and evaluation are rarely addressed though they play key roles in just how HMMs perform. Without addressing these issues it can be readily shown that a so-called HMM model may actually be a Bayesian classifer or Markov Chain. In this paper we develop method...

Distributions of triplets in some genetic sequences are examined and found to be well described by a 2-parameter Markov process with a sparse transition matrix. The variances of all the relevant parameters are not large, indicating that most sequences gather in a small region in the parameter space. Different sequences have very similar values of the entropy calculated directly from the data an...

Hidden Markov Models are widely used in speech recognition and bioinformatics systems. Conventional methods are usually used in the parameter estimation process of Hidden Markov Models (HMM). These methods are based on iterative procedure, like BaumWelch method, or gradient based methods. However, these methods can yield to local optimum parameter values. In this work, we use artificial techniq...

This paper analyzes a (1, λ)-Evolution Strategy, a randomized comparison-based adaptive search algorithm optimizing a linear function with a linear constraint. The algorithm uses resampling to handle the constraint. Two cases are investigated: first, the case where the step-size is constant, and second, the case where the step-size is adapted using cumulative step-size adaptation. We exhibit fo...

For a Markov renewal process where the time parameter is discrete, we present a novel method for calculating the asymptotic variance. Our approach is based on the key renewal theorem and is applicable even when the state space of the Markov chain is countably infinite.