scholarly journals The uniform modulus of continuity of iterated Brownian motion

1996 ◽  
Vol 9 (2) ◽  
pp. 317-333 ◽  
Author(s):  
Davar Khoshnevisan ◽  
Thomas M. Lewis
Keyword(s):  
Brownian Motion ◽  
Modulus Of Continuity ◽  
Iterated Brownian Motion ◽  
Uniform Modulus Of Continuity

scholarly journals Weighted power variations of iterated Brownian motion

2008 ◽  
Vol 13 (0) ◽  
pp. 1229-1256 ◽  
Author(s):  
Ivan Nourdin ◽  
Giovanni Peccati
Keyword(s):  
Brownian Motion ◽  
Iterated Brownian Motion

Approximation by max-product sampling Kantorovich operators with generalized kernels

2019 ◽  
pp. 1-26 ◽  
Author(s):  
Lucian Coroianu ◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Real Axis ◽  
Modulus Of Continuity ◽  
Higher Dimensions ◽  
Jackson Type ◽  
Convergence Properties ◽  
Type Estimate ◽  
Quantitative Estimates ◽  
Uniform Modulus Of Continuity ◽  
Kantorovich Operators

In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [Formula: see text] convergence, and quantitative estimates with respect to the [Formula: see text] norm, [Formula: see text]-functionals and [Formula: see text]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.

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