Probability theory and related fields, 2016-12, Vol.166 (3-4), p.801-850
2016
Details
- Autor(en) / Beteiligte
- Titel
- Infinite dimensional stochastic differential equations for Dyson’s model
- Ist Teil von
- Probability theory and related fields, 2016-12, Vol.166 (3-4), p.801-850
- Ort / Verlag
- Berlin/Heidelberg: Springer Berlin Heidelberg
- Erscheinungsjahr
- 2016
- Link zum Volltext
- Quelle
- EBSCOhost Business Source Ultimate
- Beschreibungen/Notizen
- In this paper we show the strong existence and the pathwise uniqueness of an infinite-dimensional stochastic differential equation (SDE) corresponding to the bulk limit of Dyson’s Brownian Motion, for all β ≥ 1 . Our construction applies to an explicit and general class of initial conditions, including the lattice configuration { x i } = Z and the sine process. We further show the convergence of the finite to infinite-dimensional SDE. This convergence concludes the determinantal formula of Katori and Tanemura (Commun Math Phys 293(2):469–497, 2010 ) for the solution of this SDE at β = 2 .
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0178-8051eISSN: 1432-2064DOI: 10.1007/s00440-015-0672-2Titel-ID: cdi_proquest_miscellaneous_1864577241
- Format
- –
- Schlagworte
- Brownian motion, Brownian movements, Convergence, Differential equations, Economics, Equilibrium, Finance, Formulas (mathematics), Initial conditions, Insurance, Management, Mathematical analysis, Mathematical and Computational Biology, Mathematical and Computational Physics, Mathematical models, Mathematics, Mathematics and Statistics, Operations Research/Decision Theory, Probability Theory and Stochastic Processes, Quantitative Finance, Statistics for Business, Stochastic models, Stochasticity, Studies, Texts, Theoretical