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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...
The empirical moment process is utilized to construct a family of tests for the null hypothesis that a random variable is exponentially distributed. The tests are consistent against the 'new better than used in expectation' (NBUE) class of alternatives. Consistency is shown and the limit null distribution of the test statistic is derived, while efficiency results are also provided. The finite-sample properties of the proposed procedure in comparison to more standard procedures are investigated via...
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...
Even for a well-trained statistician the construction of a histogram
for a given real-valued data set is a difficult problem. It is even
more difficult to construct a fully automatic procedure which
specifies the number and widths of the bins in a satisfactory manner
for a wide range of data sets. In this paper we compare several
histogram construction procedures by means of a simulation
study. The study includes plug-in methods, cross-validation,
penalized maximum
likelihood and the taut string...
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 (, , , ,...
The paper deals with formulation and numerical solution of problems of identification of material parameters for continuum mechanics problems in domains with heterogeneous microstructure. Due to a restricted number of measurements of quantities related to physical processes, we assume additional information about the microstructure geometry provided by CT scan or similar analysis. The inverse problems use output least squares cost functionals with values obtained from averages of state problem quantities...
The aim of this paper is to provide a gradient clustering algorithm in its complete form, suitable for direct use without requiring a deeper statistical knowledge. The values of all parameters are effectively calculated using optimizing procedures. Moreover, an illustrative analysis of the meaning of particular parameters is shown, followed by the effects resulting from possible modifications with respect to their primarily assigned optimal values. The proposed algorithm does not demand strict assumptions...
A computational framework for testing the effects of cytotoxic molecules, specific to a
given phase of the cell cycle, and vascular disrupting agents (VDAs) is presented. The
model is based on a cellular automaton to describe tumour cell states transitions from
proliferation to death. It is coupled with a model describing the tumour vasculature and
its adaptation to the blood rheological constraints when alterations are induced by VDAs
treatment....
We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...
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.
Considering the features of the fractional Klein-Kramers equation (FKKE) in phase space, only the unilateral boundary condition in position direction is needed, which is different from the bilateral boundary conditions in [Cartling B., Kinetics of activated processes from nonstationary solutions of the Fokker-Planck equation for a bistable potential, J. Chem. Phys., 1987, 87(5), 2638–2648] and [Deng W., Li C., Finite difference methods and their physical constrains for the fractional Klein-Kramers...
The invasive capability is fundamental in determining the malignancy of a solid tumor.
Revealing biomedical strategies that are able to partially decrease cancer invasiveness is
therefore an important approach in the treatment of the disease and has given rise to
multiple in vitro and in silico models. We here develop
a hybrid computational framework, whose aim is to characterize the effects of the
different cellular and subcellular mechanisms involved...
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...
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