- AutorIn
- Chiranjib Mukherjee
- Titel
- Large Deviations for Brownian Intersection Measures
- Zitierfähige Url:
- https://nbn-resolving.org/urn:nbn:de:bsz:15-qucosa-74762
- Datum der Einreichung
- 05.11.2011
- Datum der Verteidigung
- 27.07.2011
- Abstract (EN)
- We consider p independent Brownian motions in ℝd. We assume that p ≥ 2 and p(d- 2) < d. Let ℓt denote the intersection measure of the p paths by time t, i.e., the random measure on ℝd that assigns to any measurable set A ⊂ ℝd the amount of intersection local time of the motions spent in A by time t. Earlier results of Chen derived the logarithmic asymptotics of the upper tails of the total mass ℓt(ℝd) as t →∞. In this paper, we derive a large-deviation principle for the normalised intersection measure t-pℓt on the set of positive measures on some open bounded set B ⊂ ℝd as t →∞ before exiting B. The rate function is explicit and gives some rigorous meaning, in this asymptotic regime, to the understanding that the intersection measure is the pointwise product of the densities of the normalised occupation times measures of the p motions. Our proof makes the classical Donsker-Varadhan principle for the latter applicable to the intersection measure. A second version of our principle is proved for the motions observed until the individual exit times from B, conditional on a large total mass in some compact set U ⊂ B. This extends earlier studies on the intersection measure by König and Mörters.
- Freie Schlagwörter (DE)
- Grosse abweichungen, Brownsche loakler schnitzeit
- Freie Schlagwörter (EN)
- Large deviations, Brownian intersection local times
- Klassifikation (DDC)
- 500
- Normschlagwörter (GND)
- Wahrscheinlichkeitstheorie, Stochastische Prozesse
- GutachterIn
- Prof. Dr. Wolfgang Koenig
- Prof. Dr. Peter Moerters
- BetreuerIn
- Prof. Dr. Wolfgang Koenig
- Den akademischen Grad verleihende / prüfende Institution
- Universität Leipzig, Leipzig
- Max-Planck Institut fuer Mathematik in der Naturwissenschaften, Leipzig
- URN Qucosa
- urn:nbn:de:bsz:15-qucosa-74762
- Veröffentlichungsdatum Qucosa
- 18.10.2011
- Dokumenttyp
- Dissertation
- Sprache des Dokumentes
- Englisch