Integrability and Tail Estimates for Gaussian Rough Differential Equations by Thomas Cass1,
نویسندگان
چکیده
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 problems.
منابع مشابه
Integrability 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 کاملEuler Estimates for Rough Differential Equations
We consider controlled differential equations and give new estimates for higher order Euler schemes. Our proofs are inspired by recent work of A. M. Davie who considers first and second order schemes. In order to implement the general case we make systematic use of geodesic approximations in the free nilpotent group. As application, we can control moments of solutions to rough path differential...
متن کاملRelationships between Darboux Integrability and Limit Cycles for a Class of Able Equations
We consider the class of polynomial differential equation x&= , 2(,)(,)(,)nnmnmPxyPxyPxy++++2(,)(,)(,)nnmnmyQxyQxyQxy++&=++. For where and are homogeneous polynomials of degree i. Inside this class of polynomial differential equation we consider a subclass of Darboux integrable systems. Moreover, under additional conditions we proved such Darboux integrable systems can have at most 1 limit cycle.
متن کاملIsoperimetry and Rough Path Regularity
Optimal sample path properties of stochastic processes often involve generalized Hölderor variation norms. Following a classical result of Taylor, the exact variation of Brownian motion is measured in terms of ψ (x) ≡ x/ log log (1/x) near 0+. Such ψ-variation results extend to classes of processes with values in abstract metric spaces. (No Gaussian or Markovian properties are assumed.) To esta...
متن کاملSmoothness 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2013