Some limit theorems connected with Brownian local time

Raouf Ghomrasni

International Journal of Stochastic Analysis, 2006, vol. 2006, 1-5

Abstract:

Let B = ( B t ) t ≥ 0 be a standard Brownian motion and let ( L t x ; t ≥ 0 , x ∈ ℝ ) be a continuous version of its local time process. We show that the following limit lim ⁡ ε ↓ 0 ( 1 / 2 ε ) ∫ 0 t { F ( s , B s − ε ) − F ( s , B s + ε ) } d s is well defined for a large class of functions F ( t , x ) , and moreover we connect it with the integration with respect to local time L t x . We give an illustrative example of the nonlinearity of the integration with respect to local time in the random case.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:026961

DOI: 10.1155/JAMSA/2006/26961

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