We provide a construction of an implementable method based on path-independent adaptive step-size control for global approximation of jump-diffusion SDEs. The sampling points are chosen in nonadaptive way with respect...
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We provide a construction of an implementable method based on path-independent adaptive step-size control for global approximation of jump-diffusion SDEs. The sampling points are chosen in nonadaptive way with respect to trajectories of the driving Poisson and Wiener processes. However, they are adapted to the diffusion and jump coefficients of the underlying stochastic differential equation and to the values of intensity function of the driving Poisson process. The method is asymptoticallyoptimal in the class of methods that use (possibly) non-equidistant discretization of the interval [0, T] and is more efficient than any method based on the uniform mesh. (C) 2018 IMACS. Published by Elsevier B.V. All rights reserved.
Issues related to the construction of efficient algorithms for intractable discrete problems are studied. Enumeration problems are considered. Their intractability has two aspectsexponential growth of the number of th...
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Issues related to the construction of efficient algorithms for intractable discrete problems are studied. Enumeration problems are considered. Their intractability has two aspectsexponential growth of the number of their solutions with increasing problem size and the complexity of finding (enumerating) these solutions. The basic enumeration problem is the dualization of a monotone conjunctive normal form or the equivalent problem of finding irreducible coverings of Boolean matrices. For the latter problem and its generalization for the case of integer matrices, asymptotics for the typical number of solutions are obtained. These estimates are required, in particular, to prove the existence of asymptotically optimal algorithms for monotone dualization and its generalizations.
We study the m-Peripatetic Salesman Problem on random inputs. In earlier papers we proposed a polynomial asymptotically optimal algorithm for the m-PSP with different weight functions on random inputs. The probabilist...
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ISBN:
(纸本)9783319449142;9783319449135
We study the m-Peripatetic Salesman Problem on random inputs. In earlier papers we proposed a polynomial asymptotically optimal algorithm for the m-PSP with different weight functions on random inputs. The probabilistic analysis carried out for that algorithm is not suitable in the case of the m-PSP with identical weight functions. In this paper we present an approach which under certain conditions gives polynomial asymptotically optimal algorithms for the m-PSP on random inputs with identical weight functions and for the m-PSP with different weight functions, as well. We describe in detail the cases of uniform and shifted exponential distributions of random inputs.
Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and ...
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Distribution matching transforms independent and Bernoulli(1/2) distributed input bits into a sequence of output symbols with a desired distribution. Fixed-to-fixed length, invertible, and low complexity encoders and decoders based on constant composition and arithmetic coding are presented. The encoder achieves the maximum rate, namely, the entropy of the desired distribution, asymptotically in the blocklength. Furthermore, the normalized divergence of the encoder output and the desired distribution goes to zero in the blocklength.
We consider strong global approximation of SDEs driven by a homogeneous Poisson process with intensity lambda > 0. We establish the exact convergence rate of minimal errors that can be achieved by arbitrary algorit...
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We consider strong global approximation of SDEs driven by a homogeneous Poisson process with intensity lambda > 0. We establish the exact convergence rate of minimal errors that can be achieved by arbitrary algorithms based on a finite number of observations of the Poisson process. We consider two classes of methods using equidistant or nonequidistant sampling of the Poisson process, respectively. We provide a construction of optimal schemes, based on the classical Euler scheme, which asymptotically attain the established minimal errors. It turns out that methods based on nonequidistant mesh are more efficient than those based on the equidistant mesh.
The design of efficient on average algorithms for discrete enumeration problems is studied. The dualization problem, which is a central enumeration problem, is considered. New asymptoticallyoptimal dualization algori...
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The design of efficient on average algorithms for discrete enumeration problems is studied. The dualization problem, which is a central enumeration problem, is considered. New asymptoticallyoptimal dualization algorithms are constructed. It is shown that they are superior in time costs to earlier constructed asymptoticallyoptimal dualization algorithms and other available dualization algorithms with different design features.
The computational complexity of discrete problems concerning the enumeration of solutions is addressed. The concept of an asymptotically efficient algorithm is introduced for the dualization problem, which is formulat...
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The computational complexity of discrete problems concerning the enumeration of solutions is addressed. The concept of an asymptotically efficient algorithm is introduced for the dualization problem, which is formulated as the problem of constructing irreducible coverings of a Boolean matrix. This concept imposes weaker constraints on the number of "redundant" algorithmic steps as compared with the previously introduced concept of an asymptotically optimal algorithm. When the number of rows in a Boolean matrix is no less than the number of columns (in which case asymptotically optimal algorithms for the problem fail to be constructed), algorithms based on the polynomialtime-delay enumeration of "compatible" sets of columns of the matrix is shown to be asymptotically efficient. A similar result is obtained for the problem of searching for maximal conjunctions of a monotone Boolean function defined by a conjunctive normal form.
Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of...
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Asymptotic estimates for the typical number of irreducible coverings and the typical length of an irreducible covering of a Boolean matrix are obtained in the case when the number of rows is no less than the number of columns. As a consequence, asymptotic estimates are obtained for the typical number of maximal conjunctions and the typical rank of a maximal conjunction of a monotone Boolean function of variables defined by a conjunctive normal form of clauses. Similar estimates are given for the number of irredundant coverings and the length of an irredundant covering of an integer matrix (for the number of maximal conjunctions and the rank of a maximal conjunction of a two-valued logical function defined by its zero set). Results obtained previously in this area are overviewed.
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