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We design a particle interpretation of Feynman-Kac measures on path spaces
based on a backward Markovian representation combined with a traditional
mean field particle interpretation of the flow of their final time
marginals. In contrast to traditional genealogical tree based models, these
new particle algorithms can be used to compute normalized additive
functionals “on-the-fly” as well as their
limiting occupation measures with a given precision degree that does not
depend on the final time horizon.
We...
We examine different approaches to an efficient solution of the stochastic Galerkin (SG) matrix equations coming from the Darcy flow problem with different, uncertain coefficients in apriori known subdomains. The solution of the SG system of equations is usually a very challenging task. A relatively new approach to the solution of the SG matrix equations is the reduced basis (RB) solver, which looks for a low-rank representation of the solution. The construction of the RB is usually done iteratively...
In this paper some of the cointegration tests applied to a single equation are compared. Many of the existent cointegration tests are simply extensions of the unit root tests applied to the residuals of the cointegrating regression and the habitual is no cointegration. However, some non residual-based tests and some tests of the opposite null hypothesis have recently appeared in literature. Monte Carlo simulations have been used for the power comparison of the nine selected tests (, , , ,...
In this paper, we prove a Donsker theorem for one-dimensional processes generated by an operator with measurable
coefficients. We construct a random walk on any grid on the state space, using the transition probabilities of the approximated process, and the conditional average times it spends on each cell of the grid. Indeed we can compute these
quantities by solving some suitable
elliptic PDE problems.
A generic control variate method is proposed to price options under stochastic volatility models by Monte Carlo simulations. This method provides a constructive way to select control variates which are martingales in order to reduce the variance of unbiased option price estimators. We apply a singular and regular perturbation analysis to characterize the variance reduced by martingale control variates. This variance analysis is done in the regime where time scales of associated driving volatility...
With the aid of Markov Chain Monte Carlo methods we can sample even from complex multi-dimensional distributions which cannot be exactly calculated. Thus, an application to the problem of knowledge integration (e. g. in expert systems) is straightforward.
We present a Monte Carlo technique for sampling from the
canonical distribution in molecular dynamics. The method is built upon
the Nosé-Hoover constant temperature formulation and the generalized
hybrid Monte Carlo method. In contrast to standard hybrid Monte Carlo methods
only the thermostat degree of freedom is stochastically resampled
during a Monte Carlo step.
2000 Mathematics Subject Classification: 91B28, 65C05.We consider the valuation of American options using Monte
Carlo simulation, and propose a new technique which involves approximating
the optimal exercise boundary. Our method involves splitting the boundary
into a linear term and a Fourier series and using stochastic optimization in
the form of a relaxation method to calculate the coefficients in the series.
The cost function used is the expected value of the option using the the
current estimate...
We present a nonasymptotic theorem for interacting particle approximations of unnormalized Feynman–Kac models. We provide an original stochastic analysis-based on Feynman–Kac semigroup techniques combined with recently developed coalescent tree-based functional representations of particle block distributions. We present some regularity conditions under which the -relative error of these weighted particle measures grows linearly with respect to the time horizon yielding what seems to be the first...
Using the Fenchel conjugate of Phú’s Volume function F of a given essentially bounded measurable function f defined on the bounded box D ⊂ Rⁿ, the integral method of Chew and Zheng for global optimization is modified to a superlinearly convergent method with respect to the level sequence. Numerical results are given for low dimensional functions with a strict global essential supremum.
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