Smoothness of the density for solutions to Gaussian rough differential equations
نویسندگان
چکیده
منابع مشابه
Smoothness of the density for solutions to Gaussian Rough Differential Equations
We consider stochastic differential equations of the form dYt = V (Yt) dXt+V0 (Yt) dt driven by a multi-dimensional Gaussian process. Under the assumption that the vector fields V0 and V = (V1, . . . , Vd) satisfy Hörmander’s bracket condition, we demonstrate that Yt admits a smooth density for any t ∈ (0, T ], provided the driving noise satisfies certain non-degeneracy assumptions. Our analysi...
متن کاملIntegrability Estimates for Gaussian Rough Differential Equations
We derive explicit tail-estimates for the Jacobian of the solution flow for stochastic differential equations driven by Gaussian rough paths. In particular, we deduce that the Jacobian has finite moments of all order for a wide class of Gaussian process including fractional Brownian motion with Hurst parameter H > 1/4. We remark on the relevance of such estimates to a number of significant open...
متن کاملSmoothness of density for solutions to stochastic differential equations with jumps
We consider a solution xt to a generic stochastic differential equation with jumps and show that for any t0 > 0 xt0 has a C ∞ density with respect to Lebesgue measure under a uniform version of Hörmander’s conditions. Our results are proved subject to some restrictions on the rate of growth of the jump measure near zero and are accomplished using developments of traditional arguments in Malliav...
متن کاملGaussian density estimates for solutions to quasi-linear stochastic partial differential equations
In this paper we establish lower and upper Gaussian bounds for the solutions to the heat and wave equations driven by an additive Gaussian noise, using the techniques of Malliavin calculus and recent density estimates obtained by Nourdin and Viens in [19]. In particular, we deal with the one-dimensional stochastic heat equation in [0, 1] driven by the space-time white noise, and the stochastic ...
متن کاملStrong solutions to stochastic differential equations with rough coefficients
We study strong existence and pathwise uniqueness for stochastic differential equations in R with rough coefficients, and without assuming uniform ellipticity for the diffusion matrix. Our approach relies on direct quantitative estimates on solutions to the SDE, assuming Sobolev bounds on the drift and diffusion coefficients, and L bounds for the solution of the corresponding Fokker-Planck PDE,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2015
ISSN: 0091-1798
DOI: 10.1214/13-aop896