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Local limit theorems for Brownian additive functionals and penalisation of Brownian paths, IX. (English) Zbl 1219.60036

Authors’ abstract: We obtain a local limit theorem for the laws of a class of Brownian additive functionals and we apply this result to a penalisation problem. We study precisely the additive functional \(\left(A_t^- :=\int_0^t 1_{X_s <0} ds, t\geq 0\right)\). On the other hand, we describe Feynman-Kac type penalisation results for long Brownian bridges thus completing some similar previous study for standard Brownian motion [see B. Roynette, P. Vallois and M. Yor, Stud. Sci. Math. Hung. 43, No. 2, 171–246 (2006; Zbl 1121.60027)].

MSC:

60F17 Functional limit theorems; invariance principles
60G44 Martingales with continuous parameter
60J25 Continuous-time Markov processes on general state spaces
60J35 Transition functions, generators and resolvents
60J55 Local time and additive functionals
60J57 Multiplicative functionals and Markov processes
60J60 Diffusion processes
60J65 Brownian motion

Citations:

Zbl 1121.60027
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References:

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