Smoothness of Brownian local times and related functionals |
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| Authors: | D. Nualart J. Vives |
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| Affiliation: | (1) Facultat de Matemàtiques, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain;(2) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain |
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| Abstract: | In this paper we show that the local time of the Brownian motion belongs to the Sobolev space  for any p 2 and 0< <1/p. In order to prove this result we first discuss the smoothness and integrability properties of the composition of the Dirac function  with a Wiener integral W(h), and we show that this composition belongs to  , for any >0 and p>1 such that +1/p>1. |
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| Keywords: | 60J55 60H07 |
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