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Brownian penalisations related to excursion lengths. VII. (English) Zbl 1181.60046

Limiting laws, as \(t \to \infty\), for Brownian motion penalised by the longest length of excursions up to \(t\), or up to the last zero before \(t\), or again, up to the first zero after \(t\), are shown to exist, and are characterized.
For part VI, cf. ESAIM, Probab. Stat. 13, 152–180 (2009; Zbl 1189.60069).

MSC:

60F17 Functional limit theorems; invariance principles
60F99 Limit theorems in probability theory
60G17 Sample path properties
60G40 Stopping times; optimal stopping problems; gambling theory
60G44 Martingales with continuous parameter
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H20 Stochastic integral equations
60J25 Continuous-time Markov processes on general state spaces
60J55 Local time and additive functionals
60J60 Diffusion processes
60J65 Brownian motion

Citations:

Zbl 1189.60069
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References:

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[17] B. Roynette, P. Vallois and M. Yor. Penalisations of multidimensional Brownian motion, VI. To appear in ESAIM PS (2009). · Zbl 1189.60069
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