Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift

S. Menozzi; A. Pesce; X. Zhang

doi:10.1016/j.jde.2020.09.004

Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift

S. Menozzi^*, A. Pesce, X. Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Hölder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow.

Original language	English
Pages (from-to)	330-369
Number of pages	40
Journal	Journal of Differential Equations
Volume	272
DOIs	https://doi.org/10.1016/j.jde.2020.09.004
Publication status	Published - 25 Jan 2021
Externally published	Yes

Keywords

Gradient estimates
Heat kernel estimates
Parametrix method
Unbounded drift

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10.1016/j.jde.2020.09.004

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Menozzi, S., Pesce, A., & Zhang, X. (2021). Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. Journal of Differential Equations, 272, 330-369. https://doi.org/10.1016/j.jde.2020.09.004

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abstract = "We consider non degenerate Brownian SDEs with H{\"o}lder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial H{\"o}lder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow.",

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doi = "10.1016/j.jde.2020.09.004",

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T1 - Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift

AU - Menozzi, S.

AU - Pesce, A.

AU - Zhang, X.

PY - 2021/1/25

Y1 - 2021/1/25

N2 - We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Hölder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow.

AB - We consider non degenerate Brownian SDEs with Hölder continuous in space diffusion coefficient and unbounded drift with linear growth. We derive two sided bounds for the associated density and pointwise controls of its derivatives up to order two under some additional spatial Hölder continuity assumptions on the drift. Importantly, the estimates reflect the transport of the initial condition by the unbounded drift through an auxiliary, possibly regularized, flow.

KW - Gradient estimates

KW - Heat kernel estimates

KW - Parametrix method

KW - Unbounded drift

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U2 - 10.1016/j.jde.2020.09.004

DO - 10.1016/j.jde.2020.09.004

M3 - Article

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SN - 0022-0396

VL - 272

SP - 330

EP - 369

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift

Abstract

Keywords

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