Related papers: Densities for SDEs driven by degenerate $\alpha$-s…
In this paper we study the existence of densities for strongly degenerate stochastic differential equations whose coefficients depend on time and are not globally Lipschitz. In these models neither local ellipticity nor the strong…
We establish H\"older regularity and gradient estimates for the transition semigroup of the solutions to the following SDE: $$ {\rm d} X_t=\sigma (t, X_{t-}){\rm d} Z_t+b (t, X_t){\rm d} t,\ \ X_0=x\in{\mathbb R}^d, $$ where $( Z_t)_{t\geq…
In this paper we consider the following SDE with distributional drift $b$: $$ {\rm d} X_t=\sigma(X_t){\rm d} B_t+b(X_t){\rm d} t,\ X_0=x\in{\mathbb R}^d, $$ where $\sigma$ is a bounded continuous and uniformly non-degenerate $d\times…
In this paper, we show the weak and strong well-posedness of density dependent stochastic differential equations driven by $\alpha$-stable processes with $\alpha \in(1,2)$. The existence part is based on Euler's approximation as…
Let $\alpha\in(0,2)$ and $d\in{\mathbb N}$. Consider the following SDE in ${\mathbb R}^d$:$${\rm d}X_t=b(t,X_t){\rm d} t+a(t,X_{t-}){\rm d} L^{(\alpha)}_t,\ \ X_0=x,$$where $L^{(\alpha)}$ is a $d$-dimensional rotationally invariant…
Using Brownian dynamics (BD) simulations and an analytical approach we investigate the shear-induced, nonequilibrium dynamics of dense colloidal suspensions confined to a narrow slit-pore. Focusing on situations where the colloids arrange…
We investigate properties of the (conditional) law of the solution to SDEs driven by fractional Brownian noise with a singular, possibly distributional, drift. Our results on the law are twofold: i) we quantify the spatial regularity of the…
We study stochastic differential equations driven by finite-order chaos processes on abstract Wiener spaces, with pathwise Riemann-Stieltjes integration. The driving noise is an $\mathbb{R}^m$-valued chaotic process given by multiple…
By using the coupling argument, we establish the Harnack and log-Harnack inequalites for stochastic differential equations with non-Lipschitz drifts and driven by additive anisotropic subordinated Brownian motions (in particular,…
Consider the Leibenson equation \begin{equation*} \partial_t u = \Delta_p u^q, \end{equation*} where $\Delta_p f = div(|\nabla f|^{p-2}\nabla f)$ for $p>1$ and $q>0$, which is a simultaneous generalization of the porous media and the…
We present an abstract framework for establishing smoothing properties within a specific class of inhomogeneous discrete-time Markov processes. These properties, in turn, serve as a basis for demonstrating the existence of density functions…
We study a stochastic differential equation in the sense of rough path theory driven by fractional Brownian rough path with Hurst parameter H (1/3 < H <= 1/2) under the ellipticity assumption at the starting point. In such a case, the law…
The stochastic partial differential equation analyzed in this work is the Cahn-Hilliard equation perturbed by an additive fractional white noise (fractional in time and white in space). We work in the case of one spatial dimension and apply…
In this paper we study the effect of stochastic perturbations on a common type of moving boundary value PDE's which endorse Stefan boundary conditions, or Stefan problems, and show the existence and uniqueness of the solutions to a number…
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…
For $\alpha \in (1,2)$, we study the following stochastic differential equation driven by a non-degenerate symmetric $\alpha$-stable process in $\mathbb{R}^d$: \begin{align*} {\rm d} X_t=b(t,X_t){\mathord{{\rm d}}}…
In this paper Fokker-Planck-Kolmogorov type equations associated with stochastic differential equations driven by a time-changed fractional Brownian motion are derived. Two equivalent forms are suggested. The time-change process considered…
In this paper, the existence and uniqueness of the distribution dependent SDEs with H\"{o}lder continuous drift driven by $\alpha$-stable process is investigated. Moreover, by using Zvonkin type transformation, the convergence rate of…
We consider the class of non-linear stochastic partial differential equations studied in \cite{conusdalang}. Equivalent formulations using integration with respect to a cylindrical Brownian motion and also the Skorohod integral are…
In this paper we study the existence of densities for strongly degenerate stochastic differential equations (SDEs) whose coefficients depend on time and are not globally Lipschitz. In these models neither local ellipticity nor the strong…