Articles from many of the main contributors to recent progress in stochastic analysis are included in this volume, which provides a snapshot of the current state of the area and its ongoing developments. It constitutes the proceedings of the conference on ‘Stochastic Analysis and Applications’ held at the University of Oxford and the Oxford-Man Institute during 23-27 September, 2013. The conference honored the 60th birthday of Professor Terry Lyons FLSW FRSE FRS, Wallis Professor of Mathematics, University of Oxford. Terry Lyons is one of the leaders in the field of stochastic analysis. His introduction of the notion of rough paths has revolutionized the field, both in theory and in practice.
Stochastic Analysis is the branch of mathematics that deals with the analysis of dynamical systems affected by noise. It emerged as a core area of mathematics in the late 20th century and has subsequently developed into an important theory with a wide range of powerful and novel tools, and with impressive applications within and beyond mathematics. Many systems are profoundly affected by stochastic fluctuations and it is not surprising that the array of applications of Stochastic Analysis is vast and touches on many aspects of life.
The present volume is intended for researchers and Ph.D. students in stochastic analysis and its applications, stochastic optimization and financial mathematics, as well as financial engineers and quantitative analysts.
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Dan Crisan, Ben Hambly, Thaleia Zariphopoulou: Introduction to the volume.- Shigeki Aida, Wong-Zakai: Approximation of solutions to reflecting stochastic differential equations on domains in Euclidean spaces II.- Dominique Bakry: Symmetric diffusions with polynomial eigenvectors.- Erich Baur, Jean Bertoin: Cutting edges at random in large recursive trees.- René Carmona, Francois Delarue: The Master Equation for Large Population Equilibriums.- Thomas Cass, Martin Clark, Dan Crisan: The filtering equations revisited.- Ana Bela Cruzeiro, Remi Lassalle: On the Stochastic Least Action Principle for the Navier-Stokes Equation.- Alexander Davie: KMT theory applied to approximations of SDE.- Joscha Diehl, Peter Friz, Harald Oberhauser: Regularity theory for rough partial differential equations and parabolic comparison revisited.- Yidong Dong, Ronnie Sircar: Time-Inconsistent Portfolio Investment Problems.- K.D. Elworthy: Decompositions of diffusion operators and related couplings.- Hans Föllmer, Claudia Klüppelberg: Spatial Risk Measures: Local Specification and Boundary Risk.- Masatoshi Fukushima, Hiroshi Kaneko: On Villat’s kernels and BMD Schwarz kernels in Komatu-Loewner equations.- Tomoyuki Ichiba, Ioannis Karatzas: Skew-Unfolding the Skorokhod Reflection of a Continuous Semimartingale.- David Nualart: Normal approximation on a finite Wiener chaos.- Zhenjie Ren, Nizar Touzi, Jianfeng Zhang: An Overview of Viscosity Solutions of Path-Dependent PDEs.- Marta Sanz-Sole, Andre Suess: Logarithmic asymptotics of the densities of SPDEs driven by spatially correlated noise.
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