Regularization of differential equations by two fractional noises

David Nualart; Ercan Sönmez

doi:10.1142/s0219493722500290

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arXiv · 2104.14971

Regularization of differential equations by two fractional noises

David Nualart·Ercan Sönmez

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Abstract

In this paper we show the existence and uniqueness of a solution for a stochastic differential equation driven by an additive noise which is the sum of two fractional Brownian motions with different Hurst parameters. The proofs are based on the techniques of fractional calculus and Girsanov theorem. In particular, we show that the regularization effect of the fractional Brownian motion with the smaller Hurst index dominates.

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BibTeX RIS

David Nualart, Ercan Sönmez. 2021-04-30. Regularization of differential equations by two fractional noises. https://doi.org/10.1142/s0219493722500290

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