Abstract
Let B t be a one dimensional Brownian motion, and let α′ denote the derivative of the intersection local time of B t as defined by J. Rosen in [2]. The object of this paper is to prove the following formula
which was given as a formal identity in [2] without proof.
Keywords
- Brownian Motion
- Local Time
- Formal Identity
- Eral Form
- Dominate Convergence Theorem
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References
Revuz, D., Yor, M. (1986) Continuous Martingales and Brownian Motion Springer, Berlin.
Rosen, J. (2005). Derivatives of self-intersection local times, Séminaire de Probabilités, XXXVIII, Springer-Verlag, New York, LNM 1857, 171–184.
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Markowsky, G. (2008). Proof of a Tanaka-like formula stated by J. Rosen in Séminaire XXXVIII. In: Donati-Martin, C., Émery, M., Rouault, A., Stricker, C. (eds) Séminaire de Probabilités XLI. Lecture Notes in Mathematics, vol 1934. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77913-1_9
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DOI: https://doi.org/10.1007/978-3-540-77913-1_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77912-4
Online ISBN: 978-3-540-77913-1
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