Chapter 4 is removed from the thesis due to publisher restrictions.
Chapter 2 / Paper I: A Variational Approach to the construction and Malliavin Differentiability of Strong solutions of SDE’s. Olivier Menoukeu-Pamen, Thilo Meyer-Bandis, Torstein Nilssen, Frank Proske and Tusheng Zang. Published in Mathematische Annalen, Vol. 357, Issue 2, pp 761-799, 2013 doi:10.1007/s00208-013-0916-3. The final publication is available at link.springer.com. Also available as UiO Preprint series Pure mathematics 2011:09 http://urn.nb.no/URN:NBN:no-29103
Chapter 3 / Paper II: Sobolev Differentiable Stochastic Flows for SDE’s with Singluar Coefficients: Applications to the Transport Equation. Salah Mohammed, Torstein Nilssen and Frank Proske. Preprint. Available as UiO Preprint series Pure mathematics 2012:07 http://urn.nb.no/URN:NBN:no-33282
Chapter 4 / Paper III: Regularity of Strong Solutions of one-dimensional SDE’s with discontinuous and unbounded drift. Torstein Nilssen. Preprint.
Chapter 5 / Paper IV: Malliavin differentiability and strong solutions for a class of SDE in Hilbert spaces. Franco Flandoli, Torstein Nilssen and Frank Proske. Preprint. Available as UiO Preprint series Pure mathematics 2013:11. http://urn.nb.no/URN:NBN:no-29766