FRACTIONAL S(P)DES: THEORY, NUMERICS, AND OPTIMAL CONTROL (eBook)

Theory, Numerics, and Optimal Control

Wilfried Grecksch, Hannelore Lisei (Herausgeber)

eBook Download: EPUB

2025
288 Seiten
World Scientific Publishing Company (Verlag)
978-981-98-0211-1 (ISBN)

Infos

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.

Contents:

• Preface
• About the Editors
• About the Contributors
• State-of-the-Art Numerical Schemes for Solving Rough Differential Equations (Martin Redmann and Justus Werner)
• Mild Solutions to Semilinear Rough Partial Differential Equations (Stefan Tappe)
• Fractional Noise-Perturbed Nonlinear Schrödinger Equations: Stochastic Minimization Problems (Wilfried Grecksch and Hannelore Lisei)
• Calibration of Non-Semimartingale Models: An Adjoint Approach (Christian Bender and Matthias Thiel)
• Strong Convergence Analysis of a Fractional Exponential Integrator and Finite Element Method for Time-Fractional SPDEs Driven by Gaussian and Non-Gaussian Noises (Aurelien Junior Noupelah and Antoine Tambue)
• Index

Readership: Graduate students, researchers and practitioners in the fields of stochastics, numerics, physics, and finance. Secondarily, scientists with a strong background in mathematics, and undergraduate students in the field of applied mathematics.

Produkt-Details

• Erscheint lt. Verlag: 3.6.2025
• Verlagsort: Singapore
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Schlagworte: backward stochastic differential equations • Financial Markets Driven by Fractional Brownian Motion • Fractional Brownian motion • Multifractional Brownian Motion • Numerics of Stochastic Partial Differential Equations • Optimal Control of Stochastic Systems • Rough Partial Differential Equations • Rough Paths • stochastic partial differential equations • stochastic Schrödinger equation • Time-fractional Derivatives
• ISBN-10: 981-98-0211-3 / 9819802113
• ISBN-13: 978-981-98-0211-1 / 9789819802111