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When a diffusion is ergodic its transition density converges to its invariant density, see Durrett (1998). This convergence enabled us to introduce a sample partitioning technique that gives in each sub-sample, maximum likelihood estimators. The averages of these being a natural choice as estimators. To compare our estimators with the optimal we obtained from martingale estimating functions, see Sørensen (1998), we used the Ornstein-Uhlenbeck process for which exact simulations can be carried out....
Seasonal forcing is identified as a key pattern generating mechanism in an
epidemic model of rabies dispersal. We reduce an established individual-based high-detail model
down to a deterministic conceptual model. The characteristic wave pattern characterized by
high densities of infected individuals is maintained throughout the reduction process. In our
model it is evident that seasonal forcing is the dominant factor that drives pattern formation.
In particular we show that seasonal forcing can...
The singular mixed linear model with constraints is investigated with respect to an influence of inaccurate variance components on a decrease of the confidence level. The algorithm for a determination of the boundary of the insensitivity region is given. It is a set of all shifts of variance components values which make the tolerated decrease of the confidence level only. The problem about geometrical characterization of the confidence domain is also presented.
The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures....
We propose a sequential monitoring scheme for detecting a change in scale. We consider a stable historical period of length . The goal is to propose a test with asymptotically small probability of false alarm and power 1 as the length of the historical period tends to infinity. The asymptotic distribution under the null hypothesis and consistency under the alternative hypothesis is derived. A small simulation study illustrates the finite sample performance of the monitoring scheme.
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...
We consider the approximate Euler scheme for Lévy-driven stochastic differential equations. We study the rate of convergence in law of the paths. We show that when approximating the small jumps by Gaussian variables, the convergence is much faster than when simply neglecting them. For example, when the Lévy measure of the driving process behaves like |z|−1−αdz near 0, for some α ∈ (1,2), we obtain an error of order 1/√n with a computational cost of order nα. For a similar error when neglecting the...
We consider the approximate Euler scheme for Lévy-driven
stochastic differential equations.
We study the rate of convergence in law of the paths.
We show that when approximating the small jumps by Gaussian
variables, the convergence is much faster than when simply
neglecting them.
For example, when the Lévy measure of the driving process
behaves like |z|−1−αdz near 0, for some α∈ (1,2), we obtain an error of order 1/√n with a computational cost of order nα. For a similar error when neglecting the...
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...
In model search procedures for multidimensional contingency tables many different measures are used for decision for the goodness of model search, for instance , AIC or . 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...
Markov chain usage models were successfully used to model systems and software. The most prominent approaches are the so-called failure state models Whittaker and Thomason (1994) and the arc-based Bayesian models Sayre and Poore (2000). In this paper we propose arc-based semi-Markov usage models to test systems. We extend previous studies that rely on the Markov chain assumption to the more general semi-Markovian setting. Among the obtained results we give a closed form representation of the first...
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