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Simple Monte Carlo integration with respect to Bernoulli convolutions

David M. Gómez, Pablo Dartnell (2012)

Applications of Mathematics

We apply a Markov chain Monte Carlo method to approximate the integral of a continuous function with respect to the asymmetric Bernoulli convolution and, in particular, with respect to a binomial measure. This method---inspired by a cognitive model of memory decay---is extremely easy to implement, because it samples only Bernoulli random variables and combines them in a simple way so as to obtain a sequence of empirical measures converging almost surely to the Bernoulli convolution. We give explicit...

Simulation of transient performance measures for stiff markov chains

Abdelaziz Nasroallah (2010)

RAIRO - Operations Research

We consider the simulation of transient performance measures of high reliable fault-tolerant computer systems. The most widely used mathematical tools to model the behavior of these systems are Markov processes. Here, we deal basically with the simulation of the mean time to failure (MTTF) and the reliability, R(t), of the system at time t. Some variance reduction techniques are used to reduce the simulation time. We will combine two of these techniques: Importance Sampling and Conditioning...

Simulation studies on model search in 3 -dimensional contingency tables. Preliminary results

Malte Bismarck, Christel Deutschmann, Dana Králová (1990)

Aplikace matematiky

In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance α , AIC or R 2 . Simulation studies should give us an insight into the behaviour of the measures with respect to the data, the sample size, the number of degrees of freedom and the probability given distribution. To this end different log-linear models for 3-dimensional contingency tables were given and then 1,000 contingency tables were simulated...

Sparse finite element methods for operator equations with stochastic data

Tobias von Petersdorff, Christoph Schwab (2006)

Applications of Mathematics

Let A V → V ' be a strongly elliptic operator on a d -dimensional manifold D (polyhedra or boundaries of polyhedra are also allowed). An operator equation A u = f with stochastic data f is considered. The goal of the computation is the mean field and higher moments ℳ 1 u ∈ V , ℳ 2 u ∈ V ⊗ V , ... , ℳ k u ∈ V ⊗ ⋯ ⊗ V of the solution. We discretize the mean field problem using a FEM with hierarchical basis and N degrees of freedom. We present a Monte-Carlo algorithm and a deterministic algorithm for the approximation of the moment ℳ k u for k ≥ 1 . The key tool...

Stable hypothesis for mixed models with balanced cross-nesting

Dário Ferreira, João Tiago Mexia, Sandra Saraiva Ferreira (2005)

Discussiones Mathematicae Probability and Statistics

Stable hypothesis are hypothesis that may refer either for the fixed part or for the random part of the model. We will consider such hypothesis for models with balanced cross-nesting. Generalized F tests will be derived. It will be shown how to use Monte-Carlo methods to evaluate p-values for those tests.

The Kendall theorem and its application to the geometric ergodicity of Markov chains

Witold Bednorz (2013)

Applicationes Mathematicae

We give an improved quantitative version of the Kendall theorem. The Kendall theorem states that under mild conditions imposed on a probability distribution on the positive integers (i.e. a probability sequence) one can prove convergence of its renewal sequence. Due to the well-known property (the first entrance last exit decomposition) such results are of interest in the stability theory of time-homogeneous Markov chains. In particular this approach may be used to measure rates of convergence of...

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