In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that min ≤z≤t B(z) > v with u> v. The limiting process for u↓ v is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.
Some Results on the Brownian Meander with Drift / Iafrate, F.; Orsingher, E.. - In: JOURNAL OF THEORETICAL PROBABILITY. - ISSN 0894-9840. - (2019). [10.1007/s10959-019-00891-3]
Some Results on the Brownian Meander with Drift
Iafrate F.;Orsingher E.
2019
Abstract
In this paper we study the drifted Brownian meander that is a Brownian motion starting from u and subject to the condition that min ≤z≤t B(z) > v with u> v. The limiting process for u↓ v is analysed, and the sufficient conditions for its construction are given. We also study the distribution of the maximum of the meander with drift and the related first-passage times. The representation of the meander endowed with a drift is provided and extends the well-known result of the driftless case. The last part concerns the drifted excursion process the distribution of which coincides with the driftless case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
