Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths

Benjamin Gess (), Cheng Ouyang () and Samy Tindel ()
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Benjamin Gess: Max Planck Institute for Mathematics in the Sciences
Cheng Ouyang: University of Illinois at Chicago
Samy Tindel: Purdue University

Journal of Theoretical Probability, 2020, vol. 33, issue 2, 611-648

Abstract: Abstract We consider finite-dimensional rough differential equations driven by centered Gaussian processes. Combining Malliavin calculus, rough paths techniques and interpolation inequalities, we establish upper bounds on the density of the corresponding solution for any fixed time $$t>0$$t>0. In addition, we provide Varadhan estimates for the asymptotic behavior of the density for small noise. The emphasis is on working with general Gaussian processes with covariance function satisfying suitable abstract, checkable conditions.

Keywords: Fractional Brownian motion; Gaussian processes; Rough paths; Malliavin calculus; 60G15; 60H07; 60H10; 65C30 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10959-019-00967-0

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