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51.
Franziska Kühn 《Mathematische Nachrichten》2019,292(2):358-376
We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results. 相似文献
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Ball convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the convergence ball. This ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the convergence ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the convergence criteria complete this study. 相似文献
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In this short paper, we consider the long time behaviors of the fractional Heisenberg equation and the existence of a global weak attractor is proved for the shift dynamics in the path space. The key ingredient is some new type of commutator structure introduced in this paper, which seems indispensable in proving the compactness of the dynamics. The technique introduced in this paper may also be useful to other fractional order partial differential equations. 相似文献
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In this paper, we establish uniform-in-bandwidth limit laws of the logarithm for nonparametric Inverse Probability of Censoring
Weighted (I.P.C.W.) estimators of the multivariate regression function under random censorship. A similar result is deduced
for estimators of the conditional distribution function. The uniform-in-bandwidth consistency for estimators of the conditional
density and the conditional hazard rate functions are also derived from our main result. Moreover, the logarithm laws we establish
are shown to yield almost sure simultaneous asymptotic confidence bands for the functions we consider. Examples of confidence
bands obtained from simulated data are displayed.
相似文献
59.
On doubling metric measure spaces endowed with a strongly local regular Dirichlet form, we show some characterisations of pointwise upper bounds of the heat kernel in terms of global scale-invariant inequalities that correspond respectively to the Nash inequality and to a Gagliardo–Nirenberg type inequality when the volume growth is polynomial. This yields a new proof and a generalisation of the well-known equivalence between classical heat kernel upper bounds and relative Faber–Krahn inequalities or localised Sobolev or Nash inequalities. We are able to treat more general pointwise estimates, where the heat kernel rate of decay is not necessarily governed by the volume growth. A crucial role is played by the finite propagation speed property for the associated wave equation, and our main result holds for an abstract semigroup of operators satisfying the Davies–Gaffney estimates. 相似文献
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