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Density and gradient estimates for non degenerate Brownian SDEs with unbounded measurable drift. (English) Zbl 1469.60192

Based on author’s abstract: In this paper, a type of non-degenerate Brownian SDEs with Hölder continuous in space diffusion coefficients and unbounded drift with linear growth is considered by the authors. The authors obtain 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. Above all, by the unbounded drift through an auxiliary, possibly regularized, flow, the estimates reflect the transport of the initial condition well.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
35K10 Second-order parabolic equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
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