Abstract
We show that the renormalized self-intersection local time \(\gamma_t(x)\) for both the Brownian motion and symmetric stable process in R1 is differentiable in the spatial variable and that \(\gamma'_t(0)\) can be characterized as the continuous process of zero quadratic variation in the decomposition of a natural Dirichlet process. This Dirichlet process is the potential of a random Schwartz distribution. Analogous results for fractional derivatives of self-intersection local times in R1 and R2 are also discussed.
Jay Rosen: This research was supported, in part, by grants from the National Science Foundation and PSC-CUNY.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin/Heidelberg
About this chapter
Cite this chapter
Rosen, J. (2005). Derivatives of Self-intersection Local Times. In: Émery, M., Ledoux, M., Yor, M. (eds) Séminaire de Probabilités XXXVIII. Lecture Notes in Mathematics, vol 1857. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31449-3_18
Download citation
DOI: https://doi.org/10.1007/978-3-540-31449-3_18
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23973-4
Online ISBN: 978-3-540-31449-3
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)