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).
For part VI, cf. ESAIM, Probab. Stat. 13, 152–180 (2009; Zbl 1189.60069).
Reviewer: Pavel Gapeev (London)
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 1189.60069References:
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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 · doi:10.1051/ps:2008003 |
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