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Approximating functions on stratified sets

Authors: D. Drusvyatskiy and M. Larsson
Journal: Trans. Amer. Math. Soc. 367 (2015), 725-749
MSC (2010): Primary 26B05; Secondary 14B05, 15A18, 57N80, 60J99
Published electronically: July 29, 2014
MathSciNet review: 3271275
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Abstract: We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochastic processes, called the matrix-valued Bessel processes.

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Additional Information

D. Drusvyatskiy
Affiliation: Department of Mathematics, University of Washington, Seattle, Washington 98195-4350 — and — Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

M. Larsson
Affiliation: Swiss Finance Institute, École Polytechnique Fédérale de Lausanne, Switzerland

Keywords: Stratification, stratified vector field, approximation, normal bundle, Bessel process, Sobolev space
Received by editor(s): November 16, 2012
Received by editor(s) in revised form: August 15, 2013
Published electronically: July 29, 2014
Additional Notes: The first author’s research was made with Government support under and awarded by DoD, Air Force Office of Scientific Research, National Defense Science and Engineering Graduate (NDSEG) Fellowship, 32 CFR 168a
The second author gratefully acknowledges funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013) / ERC Grant Agreement n. 307465-POLYTE
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