Related papers: Weak solutions for singular multiplicative SDEs vi…
We are interested in existence of solutions to the $d$-dimensional equation \begin{equation*} X_t=x_0+\int_0^t b(X_s)ds + B_t, \end{equation*} where $B$ is a (fractional) Brownian motion with Hurst parameter $H\leqslant 1/2$ and $b$ is an…
We consider the numerical approximation of the mild solution to a semilinear stochastic wave equation driven by additive noise. For the spatial approximation we consider a standard finite element method and for the temporal approximation, a…
We establish the existence of weak solutions to a class of distribution-dependent stochastic differential equations (DDSDEs) with possibly degenerate multiplicative noise and singular coefficients. Extending the weak existence techniques…
We study stochastic partial differential equations (SPDEs) with potentially very rough fractional noise with Hurst parameter $H\in(0,1)$. Close to a change of stability measured with a small parameter $\varepsilon$, we rely on the natural…
For an SDE driven by a rotationally invariant $\alpha$-stable noise we prove weak uniqueness of the solution under the balance condition $\alpha+\gamma>1$, where $\gamma$ denotes the Holder index of the drift coefficient. We prove existence…
In this note, we take up the study of weak convergence for stochastic differential equations driven by a (Liouville) fractional Brownian motion $B$ with Hurst parameter $H\in(1/3,1/2)$. In the current paper, we approximate the…
We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equation driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an…
We investigate the validity and accuracy of weak-noise (saddle-point or instanton) approximations for piecewise-smooth stochastic differential equations (SDEs), taking as an illustrative example a piecewise-constant SDE, which serves as a…
In this paper, we establish the strong well-posedness of SDEs with merely integrable time-dependent drifts driven by fractional Brownian motions with Hurst parameter H<1/2. Our result holds over the entire subcritical regime and can be…
We study a general class of singular degenerate parabolic stochastic partial differential equations (SPDEs) which include, in particular, the stochastic porous medium equations and the stochastic fast diffusion equation. We propose a fully…
In this paper, we establish concentration inequalities both for functionals of the whole solution on an interval [0, T ] of an additive SDE driven by a fractional Brownian motion with Hurst parameter H $\in$ (0, 1) and for functionals of…
We study distribution dependent stochastic differential equations with irregular, possibly distributional drift, driven by an additive fractional Brownian motion of Hurst parameter $H\in (0,1)$. We establish strong well-posedness under a…
We consider a particle system with a mean-field-type interaction perturbed by some common and individual noises. When the interacting kernels are sublinear and only locally Lipschitz-continuous, relying on arguments based on the tightness…
We investigate the well-posedness of stochastic differential equations driven by fractional Brownian motion, focusing on the long-range dependent case $H \in (\frac{1}{2}, 1)$. While existing results on regularization by such noise…
We consider a differential equation driven by a Brownian motion as well as a rough path. We prove a Girsanov-type result for this equation to construct a weak solution in the probabilistic sense.
We study the ergodic properties of finite-dimensional systems of SDEs driven by non-degenerate additive fractional Brownian motion with arbitrary Hurst parameter $H\in(0,1)$. A general framework is constructed to make precise the notions of…
We construct solutions to Burgers type equations perturbed by a multiplicative space-time white noise in one space dimension. Due to the roughness of the driving noise, solutions are not regular enough to be amenable to classical methods.…
We study the long-time behaviour of solutions to a class of $d$-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst parameter $H \in (0,1)$. The drift consists of a dissipative Lipschitz term and a…
We highlight a fundamental ill-posedness issue for nonlinear stochastic wave equations driven by a fractional noise. Namely, if the noise becomes too rough (i.e., the sum of its Hurst indexes becomes too small), then there is essentially no…
In this paper we show that under some assumptions, for a $d$-dimensional fractional Brownian motion with Hurst parameter $H>1/2$, the density of solution of stochastic differential equation driven by it has a short-time expansion similar to…