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

Gess B, Ouyang C, Tindel S (2020)
JOURNAL OF THEORETICAL PROBABILITY 33(2): 611-648.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Autor*in
Gess, BenjaminUniBi; Ouyang, Cheng; Tindel, Samy
Abstract / Bemerkung
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>0In 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.
Stichworte
Fractional Brownian motion; Gaussian processes; Rough paths; Malliavin; calculus
Erscheinungsjahr
2020
Zeitschriftentitel
JOURNAL OF THEORETICAL PROBABILITY
Band
33
Ausgabe
2
Seite(n)
611-648
ISSN
0894-9840
eISSN
1572-9230
Page URI
https://pub.uni-bielefeld.de/record/2943573

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Gess B, Ouyang C, Tindel S. Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths. JOURNAL OF THEORETICAL PROBABILITY. 2020;33(2):611-648.
Gess, B., Ouyang, C., & Tindel, S. (2020). Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths. JOURNAL OF THEORETICAL PROBABILITY, 33(2), 611-648. doi:10.1007/s10959-019-00967-0
Gess, B., Ouyang, C., and Tindel, S. (2020). Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths. JOURNAL OF THEORETICAL PROBABILITY 33, 611-648.
Gess, B., Ouyang, C., & Tindel, S., 2020. Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths. JOURNAL OF THEORETICAL PROBABILITY, 33(2), p 611-648.
B. Gess, C. Ouyang, and S. Tindel, “Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths”, JOURNAL OF THEORETICAL PROBABILITY, vol. 33, 2020, pp. 611-648.
Gess, B., Ouyang, C., Tindel, S.: Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths. JOURNAL OF THEORETICAL PROBABILITY. 33, 611-648 (2020).
Gess, Benjamin, Ouyang, Cheng, and Tindel, Samy. “Density Bounds for Solutions to Differential Equations Driven by Gaussian Rough Paths”. JOURNAL OF THEORETICAL PROBABILITY 33.2 (2020): 611-648.