General Transfer Formula for Stochastic Integral with Respect to Multifractional Brownian Motion

Christian Bender (), Joachim Lebovits () and Jacques Lévy Véhel ()
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Christian Bender: Saarland University
Joachim Lebovits: Laboratoire Analyse, Géométrie et Applications C.N.R.S. (UMR 7539), Université Sorbonne Paris Nord
Jacques Lévy Véhel: 5 rue Olympe de Gouges

Journal of Theoretical Probability, 2024, vol. 37, issue 1, 905-932

Abstract: Abstract In this work we show how results from stochastic integration with respect to multifractional Brownian motion (mBm) can be simply deduced from results of stochastic integration with respect to fractional Brownian motion (fBm), by using a “Transfer Principle”. To illustrate this fact, we prove an Itô formula for integral with respect to mBm by deriving it from Itô formula for integral with respect to fBm, of any Hurst index H in (0, 1).

Keywords: Fractional and multifractional Brownian motions; White Noise theory; Wick–Itô integral; 60H40; 60G22; 60H05 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-023-01258-5

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