Print Email Facebook Twitter Analysis of infinite dimensional diffusions Title Analysis of infinite dimensional diffusions Author Maas, J. Contributor Van Neerven, J.M.A.M. (promotor) Faculty Electrical Engineering, Mathematics and Computer Science Date 2009-04-21 Abstract Stochastic processes in infinite dimensional state spaces provide a mathematical description of various phenomena in physics, population biology, finance, and other fields of science. Several aspects of these processes have been studied in this thesis by means of new analytic methods. Firstly, Kolmogorov equations associated with a class of infinite dimensional diffusions are considered. In this thesis the problem of obtaining domain characterisations for the generators is solved in the infinite dimensional non-symmetric case. Secondly, Fokker-Planck equations associated with infinite dimensional diffusions are studied. It is shown that these equations can be interpreted as gradient flows in the space of probability measures over an infinite dimensional Banach space. Finally, the thesis deals with Malliavin calculus, a very useful calculus for obtaining regularity results for stochastic (partial) differential equations. So far the theory has been restricted to Hilbert spaces, but it is demonstrated in this thesis that the theory extends to more general Banach spaces. Subject infinite dimensional diffusionsgradient flowsmalliavin calculuselliptic operatorsriesz transformsfokker-planck equations To reference this document use: http://resolver.tudelft.nl/uuid:5e1071d4-9462-40f4-8673-ae24cb9ee475 ISBN 978-90-9024094-7 Part of collection Institutional Repository Document type doctoral thesis Rights (c) 2009 Maas, J. Files PDF maas_20090421.pdf 1.22 MB Close viewer /islandora/object/uuid:5e1071d4-9462-40f4-8673-ae24cb9ee475/datastream/OBJ/view