Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients

Suo, Yongqiang; Yuan, Chenggui; Zhang, shaoqin

doi:10.48550/arxiv.1907.02293

Cited by 2 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparatively little is known for purely fractional SDEs, i.e. b ≡ 0, with discontinuous drift coefficient; see [1,13,25] for the case H > 1 2 . In [13, Theorem 3.5.14] the existence of a strong solution is proven for purely fractional SDEs with additive noise, where the drift coefficient is given by the discontinuous function a(x) = sign (x) for all x ∈ R and the Hurst index H is restricted to H ∈ 1 2 , (1 + √ 5)/4 ; see also [14, Theorem 1] for a related result.…”

Section: Introductionmentioning

confidence: 99%

On mixed fractional stochastic differential equations with discontinuous drift coefficient

Sönmez

2022

J. Appl. Probab.

View full text Add to dashboard Cite

We prove existence and uniqueness for the solution of a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with an absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.

show abstract

Section: Introductionmentioning

confidence: 99%

On mixed fractional stochastic differential equations with discontinuous drift coefficient

Sönmez

2022

J. Appl. Probab.

View full text Add to dashboard Cite

show abstract

“…Comparatively little is know for purely fractional SDEs, i.e. b ≡ 0, with discontinuous drift coefficient, see [1,13,25] for the case H > 1 2 . In [13, Theorem 3.5.14] the existence of a strong solution is proven for purely fractional SDEs with additive noise, where the drift coefficient is given by the discontinuous function a(x) = sign(x) for all x ∈ R and the Hurst index H is restricted to…”

Section: Introductionmentioning

confidence: 99%

On mixed fractional SDEs with discontinuous drift coefficient

Sönmez¹

2020

Preprint

View full text Add to dashboard Cite

We prove existence and uniqueness of the solution for a class of mixed fractional stochastic differential equations with discontinuous drift driven by both standard and fractional Brownian motion. Additionally, we establish a generalized Itô rule valid for functions with absolutely continuous derivative and applicable to solutions of mixed fractional stochastic differential equations with Lipschitz coefficients, which plays a key role in our proof of existence and uniqueness. The proof of such a formula is new and relies on showing the existence of a density of the law under mild assumptions on the diffusion coefficient.

show abstract

Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients

Cited by 2 publications

References 23 publications

On mixed fractional stochastic differential equations with discontinuous drift coefficient

On mixed fractional stochastic differential equations with discontinuous drift coefficient

On mixed fractional SDEs with discontinuous drift coefficient

Contact Info

Product

Resources

About