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

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Backward Stochastic Differential Equations
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Category=PBWL
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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 SchrAfA?dinger Equation
Stochastic Schrodinger Equation
Stochastic Schrödinger Equation
Time-fractional Derivatives

Product details

  • ISBN 9789819802098
  • Publication Date: 15 Jul 2025
  • Publisher: World Scientific Publishing Co Pte Ltd
  • Publication City/Country: SG
  • Product Form: Hardback
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Description
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.