Adopting Feynman–Kac Formula in Stochastic Differential Equations with (Sub-)Fractional Brownian Motion

نویسندگان

چکیده

The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) stochastic (SDEs) wider class processes, including Brownian motions {BtH,t≥0} sub-fractional {ξtH,t≥0} with Hurst parameter H∈(12,1). We start by establishing the connection fPDE SDE via Feynman–Kac Theorem, which provides representation general Cauchy problem. In hindsight, we extend assuming SDEs fractional- prove generalized formulas under (sub-)fractional motion. An application theorem demonstrates, as by-product, solution integral, has relevance in probability theory.

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ژورنال

عنوان ژورنال: Mathematics

سال: 2022

ISSN: ['2227-7390']

DOI: https://doi.org/10.3390/math10030340