An introduction to differential equations driven by rough path
Informal聽Systems聽Seminar聽(ISS) Centre聽for聽Intelligent聽Machines聽(CIM)聽and聽Groupe聽d'Etudes聽et聽de Recherche聽en聽Analyse聽des聽Decisions聽(GERAD)
Speaker: Torstein Nilssen
*Note that this is a hybrid event*
惭别别迟颈苍驳听滨顿:听845听1388听1004听听听听听听听
笔补蝉蝉肠辞诲别:听痴滨厂厂
Abstract: In this talk I will start from a differential equation and show that the deterministic聽integration聽theory聽of聽Young聽(1936)聽is聽not聽suitable聽to聽give a聽pathwise聽description聽of聽stochastic聽differential聽equations.聽I聽will聽then present聽the聽insight聽by聽Terry聽Lyons聽(1998)聽that聽the聽missing聽ingredient聽is the聽iterated聽integral聽of聽the聽Brownian聽motion聽as聽well聽as聽a聽Taylor expansion聽type聽equation聽which聽gives聽intuition聽into聽why聽this聽is聽the correct聽object.聽We聽will聽then聽consider聽the聽ansatz聽of聽controlled聽paths聽and how聽it聽can聽be聽used聽to聽set聽up聽a聽fixed聽point聽mapping聽for聽rough differential聽equations.聽If聽time聽allows聽we聽will聽look聽at聽applications聽of the聽theory聽to聽Wong-Zakai聽approximations聽and聽fractional聽Brownian聽motion.
Affiliation : Torstein Kastberg is an Associate Professor at Institue of Mathematics at University of Agder, Norway.
