Fractional S(p)des: Theory, Numerics, And Optimal Control

Recent breakthroughs in volatility modelling have brought fractional stochastic calculus to a groundbreaking position. Readers of Fractional S(P)DEs will find a unique and comprehensive overview encompassing the theory and the numerics of both ordinary and partial differential equations (SDEs and SPDEs, respectively), driven by fractional Brownian motion. Within this book, both differential equations are considered with fractional noise, while also considering fractional derivatives in the case of SPDEs. Three primary aspects are pursued: Theory and numerics for rough SPDEs; Optimal control of both SDEs and SPDEs driven by fractional Brownian motions (and their applications); And numerics for time-fractional SPDEs driven by both Gaussian and non-Gaussian noises. This series of complementary articles, compiled by two internationally renowned scientists, is united by a common application-oriented view of fractional Brownian motion and its stochastic calculus. As such, this book will be particularly useful for mathematicians working in the fields of stochastics applied in Finance and Natural Sciences, as well as those preparing courses on advanced stochastic processes.

Wilfried Grecksch is Professor Emeritus with the Martin-Luther-Universität, Halle-Wittenberg. He proposed several important approaches to the theoretical study and the numerical solution of stochastic differential equations which are not well known and widely used by researchers. He was Rector of the Martin-Luther-Universität between 2000–2006 and Director of the Institute for Mathematics between 2014–2016. Professor Grecksch is an internationally recognized expert in stochastics, SPDEs, stochastic analysis, and stochastic control theory.

Hannelore Lisei is Associate Professor with the Babeş-Bolyai University, Cluj-Napoca. She was a researcher at the Department of Mathematics at Technische Universität Berlin between 1999 and 2002, and has lectured and produced seminars on analysis there, as well as on numerical analysis, probability theory, statistics, and information theory at the Babeş-Bolyai University. Her interests are in probability theory, stochastic analysis, statistics, numerical analysis, and variational calculus.