共查询到20条相似文献,搜索用时 31 毫秒
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Ercan Sönmez 《Stochastic Processes and their Applications》2018,128(2):426-444
Let be a multivariate operator-self-similar random field with values in . Such fields were introduced in [22] and satisfy the scaling property for all , where is a real matrix and is an real matrix. We solve an open problem in [22] by calculating the Hausdorff dimension of the range and graph of a trajectory over the unit cube in the Gaussian case. In particular, we enlighten the property that the Hausdorff dimension is determined by the real parts of the eigenvalues of and as well as the multiplicity of the eigenvalues of and . 相似文献
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David Gilat Isaac Meilijson Laura Sacerdote 《Stochastic Processes and their Applications》2018,128(6):1849-1856
For a martingale starting at with final variance , and an interval , let be the normalized length of the interval and let be the normalized distance from the initial point to the lower endpoint of the interval. The expected number of upcrossings of by is at most if and at most otherwise. Both bounds are sharp, attained by Standard Brownian Motion stopped at appropriate stopping times. Both bounds also attain the Doob upper bound on the expected number of upcrossings of for submartingales with the corresponding final distribution. Each of these two bounds is at most , with equality in the first bound for . The upper bound on the length covered by during upcrossings of an interval restricts the possible variability of a martingale in terms of its final variance. This is in the same spirit as the Dubins & Schwarz sharp upper bound on the expected maximum of above , the Dubins & Schwarz sharp upper bound on the expected maximal distance of from , and the Dubins, Gilat & Meilijson sharp upper bound on the expected diameter of . 相似文献
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Effect of stochastic perturbations for front propagation in Kolmogorov Petrovskii Piscunov equations
John M. Noble 《Stochastic Processes and their Applications》2018,128(10):3531-3557
This article considers equations of Kolmogorov Petrovskii Piscunov type in one space dimension, with stochastic perturbation: where the stochastic differential is taken in the sense of Itô and is a Gaussian random field satisfying and . Two situations are considered: firstly, is simply a standard Wiener process (i.e. ): secondly, with .The results are as follows: in the first situation (standard Wiener process: i.e. ), there is a non-degenerate travelling wave front if and only if , with asymptotic wave speed ; the noise slows the wave speed. If the stochastic integral is taken instead in the sense of Stratonovich, then the asymptotic wave speed is the classical McKean wave speed and does not depend on .In the second situation (noise with spatial covariance which decays to 0 at , stochastic integral taken in the sense of Itô), a travelling front can be defined for all . Its average asymptotic speed does not depend on and is the classical wave speed of the unperturbed KPP equation. 相似文献
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Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
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《Applied Mathematics Letters》2005,18(11):1286-1292
First a general model for two-step projection methods is introduced and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let be a real Hilbert space and be a nonempty closed convex subset of . For arbitrarily chosen initial points , compute sequences and such that where is a nonlinear mapping on is the projection of onto , and . The two-step model is applied to some variational inequality problems. 相似文献
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For any polynomial f of we introduce the following characteristic of the distribution of its second order derivative, which extends the differential uniformity notion: where is the second order derivative. Our purpose is to prove a density theorem relative to this quantity, which is an analogue of a density theorem proved by Voloch for the differential uniformity. 相似文献
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L.H. Duc M.J. Garrido-Atienza A. Neuenkirch B. Schmalfuß 《Journal of Differential Equations》2018,264(2):1119-1145
This paper addresses the exponential stability of the trivial solution of some types of evolution equations driven by Hölder continuous functions with Hölder index greater than 1/2. The results can be applied to the case of equations whose noisy inputs are given by a fractional Brownian motion with covariance operator Q, provided that and is sufficiently small. 相似文献
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The -restricted arc connectivity of digraphs is a common generalization of the arc connectivity and the restricted arc connectivity. An arc subset of a strong digraph is a -restricted arc cut if has a strong component with order at least such that contains a connected subdigraph with order at least . The -restricted arc connectivity of a digraph is the minimum cardinality over all -restricted arc cuts of .Let be a strong digraph with order and minimum degree . In this paper, we first show that exists if and, furthermore, if , where is the minimum 3-degree of . Next, we prove that if . Finally, we give examples showing that these results are best possible in some sense. 相似文献
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赵晓军 《数学物理学报(B辑英文版)》2018,38(2):673-680
In this article, we study the nonexistence of solution with finite Morse index for the following Choquard type equation-△u=∫RN|u(y)|p|x-y|αdy|u(x)|p-2u(x) in RN where N ≥ 3, 0 α min{4, N}. Suppose that 2 p (2 N-α)/(N-2),we will show that this problem does not possess nontrivial solution with finite Morse index. While for p=(2 N-α)/(N-2),if i(u) ∞, then we have ∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~α dxdy ∞ and ∫_RN|▽u|~2 dx=∫_RN∫_RN|u(x)p(u)(y)~p/|x-y|~αdxdy. 相似文献
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This paper develops systematically the stochastic calculus via regularization in the case of jump processes. In particular one continues the analysis of real-valued càdlàg weak Dirichlet processes with respect to a given filtration. Such a process is the sum of a local martingale and an adapted process such that , for any continuous local martingale . Given a function , which is of class (or sometimes less), we provide a chain rule type expansion for which stands in applications for a chain Itô type rule. 相似文献
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In this work, we prove the existence of convex solutions to the following k-Hessian equation in the neighborhood of a point , where , is nonnegative near , and . 相似文献
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Shao-Yuan Huang 《Journal of Differential Equations》2018,264(9):5977-6011
In this paper, we study the classification and evolution of bifurcation curves of positive solutions for the one-dimensional Minkowski-curvature problem where , and for . Furthermore, we show that, for sufficiently large , the bifurcation curve may have arbitrarily many turning points. Finally, we apply these results to obtain the global bifurcation diagrams for Ambrosetti–Brezis–Cerami problem, Liouville–Bratu–Gelfand problem and perturbed Gelfand problem with the Minkowski-curvature operator, respectively. Moreover, we will make two lists which show the different properties of bifurcation curves for Minkowski-curvature problems, corresponding semilinear problems and corresponding prescribed curvature problems. 相似文献
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Very recently, Thomassé et al. (2017) have given an FPT algorithm for Weighted Independent Set in bull-free graphs parameterized by the weight of the solution, running in time . In this article we improve this running time to . As a byproduct, we also improve the previous Turing-kernel for this problem from to . Furthermore, for the subclass of bull-free graphs without holes of length at most for , we speed up the running time to . As grows, this running time is asymptotically tight in terms of , since we prove that for each integer , Weighted Independent Set cannot be solved in time in the class of -free graphs unless the ETH fails. 相似文献