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Stochastic differential equation driven by the Rosenblatt process | Synapse

April 10, 2026Open Access

Stochastic differential equation driven by the Rosenblatt process

Key Points

To explore one-dimensional stochastic differential equations influenced by the Rosenblatt process.
Analyzed the properties of the Rosenblatt process
Founded on the concept of non-central limit theorems
Examined the relationship with fractional Brownian motion
Identified the covariance relation between the Rosenblatt process and fractional Brownian motion
Demonstrated applicability in stochastic modeling scenarios

Abstract

The Rosenblatt process is a non-Gaussian self-similar process residing in the second Wiener chaos. It emerges as the limit of correlated random sequences in "non-central limit theorems." It shares the same covariance function as fractional Brownian motion. In this paper, we studied a class of one-dimensional stochastic differential equations driven by the Rosenblatt process with Hurst parameter 12

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Authors

S

Sakina Benkaddour

A

Abdeldjebber Kandouci

O

Omar Kebiri

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Cite this study

Benkaddour et al. (Thu,) studied this question.

www.synapsesocial.com/papers/69d894ce6c1944d70ce05c7d — DOI: https://doi.org/10.17169/refubium-51800