What question did this study set out to answer?

The aim is to develop a polynomial tensor-valued operator for fractional stochastic differential equations and analyze its properties.

March 1, 2026Open Access

Polynomial Drift in Fractional Stochastic Differential Equations

Key Points

The aim is to develop a polynomial tensor-valued operator for fractional stochastic differential equations and analyze its properties.
Introduced a polynomial tensor-valued fractional stochastic operator.
Established local wellposedness of the Volterra equation under local Lipschitz conditions.
Developed operators for drift and diffusion terms within a tensor framework.
Proved contraction of the Volterra operator on a suitable Banach space.
Showed existence and uniqueness of solutions for the model.
Demonstrated an interval of solutions that corresponds to the defined operators.
Highlighted the capacity of the tensor framework to capture complex physical interactions.

Abstract

We introduce a polynomial tensor-valued fractional stochastic operator and establish local wellposedness of the associated Volterra equation under local Lipschitz conditions. We establish properties for the FSDE forms that fit within our model by generating operators for drift and diffusion terms, and incorporating a tensor-based structure. Unlike standard FSDEs, our tensor framework explicitly captures higher-dimensional coupling and multilinear interactions required for complex physical systems. We prove that the associated Volterra operator is a contraction on a suitable Banach space, which we use to prove the existence, uniqueness, and interval of solutions for the model

Polynomial Drift in Fractional Stochastic Differential Equations

Key Points

Abstract

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