Related papers: Rough differential equations with unbounded drift …
It is widely believed that at high Reynolds number (Re) all turbulent flows approach a state of "fully developed turbulence" defined by a unique, Re-independent statistics of the velocity fluctuations. Yet direct measurements of the…
This work establishes the existence and regularity of random pullback attractors for parabolic partial differential equations with rough nonlinear multiplicative noise under natural assumptions on the coefficients. To this aim, we combine…
A stochastic linear transport equation with multiplicative noise is considered and the question of no-blow-up is investigated. The drift is assumed only integrable to a certain power. Opposite to the deterministic case where smooth initial…
Within the rough path framework we prove the continuity of the solution to random differential equations driven by fractional Brownian motion with respect to the Hurst parameter $H$ when $H \in (1/3, 1/2]$.
We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition…
In this paper, we study a multidimensional backward stochastic differential equation (BSDE) with an additional rough drift (rough BSDE), and give the existence and uniqueness of the adapted solution, either when the terminal value and the…
In this paper we study rough differential equations driven by Gaussian rough paths from the viewpoint of Malliavin calculus. Under mild assumptions on coefficient vector fields and underlying Gaussian processes, we prove that solutions at a…
We consider differential equations driven by rough paths and study the regularity of the laws and their long time behavior. In particular, we focus on the case when the driving noise is a rough path valued fractional Brownian motion with…
We consider a stochastic flow on $\mathds{R}$ generated by an SDE with its drift being a function of bounded variation. We show that the flow is differentiable with respect to the initial conditions. Asymptotic properties of the flow are…
We consider anticipative Stratonovich stochastic differential equations driven by some stochastic process lifted to a rough path. Neither adaptedness of initial point and vector fields nor commuting conditions between vector field is…
In this note we consider differential equations driven by a signal $x$ which is $\gamma$-H\"older with $\gamma>1/3$, and is assumed to possess a lift as a rough path. Our main point is to obtain existence of solutions when the coefficients…
In this paper, we investigate two hyperbolic flows obtained by adding forcing terms in direction of the position vector to the hyperbolic mean curvature flows in \cite{klw,hdl}. For the first hyperbolic flow, as in \cite{klw}, by using…
It is well-known that a stochastic differential equation (SDE) on a Euclidean space driven by a Brownian motion with Lipschitz coefficients generates a stochastic flow of homeomorphisms. When the coefficients are only locally Lipschitz,…
We establish the existence of solutions to path-dependent rough differential equations with non-anticipative coefficients. Regularity assumptions on the coefficients are formulated in terms of horizontal and vertical derivatives.
We prove a large deviation principle for the slow-fast rough differential equations under the controlled rough path framework. The driver rough paths are lifted from the mixed fractional Brownian motion with Hurst parameter $H\in…
Using the multiple stochastic integrals we prove an existence and uniqueness result for a linear stochastic equation driven by the fractional Brownian motion with any Hurst parameter. We study both the one parameter and two parameter cases.…
We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded…
In this work, we introduce a solution theory for scalar-valued rough differential equations driven by multi-indices rough paths. To achieve this task, we will show how the flow approach using the log-ODE method introduced by Bailleul fits…
We formulate the flow of thick fluids as evolution variational and quasi-variational inequalities, with a variable threshold on the absolute value of the deformation rate tensor. In the variational case, we show the existence and uniqueness…
We first prove some general results on pathwise uniqueness, comparison property and existence of nonnegative strong solutions of stochastic equations driven by white noises and Poisson random measures. The results are then used to prove the…