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The problem of estimating the number, n, of trials, given a sequence of k independent success counts obtained by replicating the n-trial experiment is reconsidered in this paper. In contrast to existing methods it is assumed here that more information than usual is available: not only the numbers of successes are given but also the number of pairs of consecutive successes. This assumption is realistic in a class of problems of spatial statistics. There typically k = 1, in which case the classical...
We propose a parallel algorithm which uses both
Monte-Carlo and quasi-Monte-Carlo methods. A detailed analysis of this
algorithm, followed by examples, shows that the estimator's efficiency
is a linear function of the processor number. As a concrete application
example, we evaluate performance measures of a multi-class queueing
network in steady state.
We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique. We will examine...
We present an interacting particle system
methodology for the numerical solving of the Lyapunov exponent
of Feynman–Kac semigroups and for estimating the principal
eigenvalue of Schrödinger generators. The continuous or discrete time
models studied in this work
consists of N interacting particles evolving in an environment
with soft obstacles related to a potential function V. These
models are related to genetic algorithms and Moran type particle
schemes. Their choice
is not unique. We...
Motivated by the development of efficient Monte Carlo methods
for PDE models in molecular dynamics,
we establish a new probabilistic interpretation of a family of divergence form
operators with discontinuous coefficients at the interface
of two open subsets of . This family of operators includes the case of the
linearized Poisson-Boltzmann equation used to
compute the electrostatic free energy of a molecule.
More precisely, we explicitly construct a Markov process whose
infinitesimal generator...
With the pioneering work of [Pardoux and Peng,
Syst. Contr. Lett.14 (1990) 55–61; Pardoux and Peng,
Lecture Notes in Control and Information Sciences176
(1992) 200–217]. We have at our disposal
stochastic processes which solve the so-called backward stochastic
differential equations. These processes provide us with a Feynman-Kac
representation for the solutions of a class of nonlinear partial differential equations (PDEs) which appear
in many applications in the field of Mathematical Finance....
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