Related papers: SDEs with supercritical distributional drifts

We study scaling limits of the weakly driven Zhang and the Bak-Tang-Wiesenfeld (BTW) model for self-organized criticality. We show that the weakly driven Zhang model converges to a stochastic partial differential equation (PDE) with…

There has been a great deal of recent interest in learning and approximation of functions that can be expressed as expectations of a given nonlinearity with respect to its random internal parameters. Examples of such representations include…

Although statistical inference in stochastic differential equations (SDEs) driven by Wiener process has received significant attention in the literature, inference in those driven by fractional Brownian motion seem to have seen much less…

Let X be the solution of the multidimensional stochastic differential equationdX(t) = b(t, X(t)) dt + sigma(t, X(t)) dW(t)\, with X(0)=x where W is a standard Brownian motion. We show that when b is measurable and sigma is in an appropriate…

Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…

We give a new approach to prove the existence of a weak solution of \[dx_t = f(t,x_t)dt + g(t)dB^H_t\] where $B^H_t$ is a fractional Brownian motion with values in a separable Hilbert space for suitable functions $f$ and $g$. Our idea is to…

In this paper we study general nonlinear stochastic differential equations, where the usual Brownian motion is replaced by a L\'evy process. We also suppose that the coefficient multiplying the increments of this process is merely Lipschitz…

In this paper, we study (strong and weak) existence and uniqueness of a class of non-Markovian SDEs whose drift contains the derivative in the sense of distributionsof a continuous function.

In this paper, we introduce a new simple approach to developing and establishing the convergence of splitting methods for a large class of stochastic differential equations (SDEs), including additive, diagonal and scalar noise types. The…

In this article, we study the stochastic aggregation-diffusion equation with a singular drift represented by a monotone radial kernel. We demonstrate the existence and uniqueness of a diffusion process that acts as a weak solution to our…

This article is devoted to the existence and uniqueness of pathwise solutions to stochastic evolution equations, driven by a H\"older continuous function with H\"older exponent in $(1/2,1)$, and with nontrivial multiplicative noise. As a…

We study stochastic differential equations (SDEs) whose drift and diffusion coefficients are path-dependent and controlled. We construct a value process on the canonical path space, considered simultaneously under a family of singular…

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…

In this paper, the stability behaviors of stochastic differential equations (SDEs) driven by time-changed Brownian motions are discussed. Based on the generalized Lyapunov method and stochastic analysis, necessary conditions are provided…

In this work we present a condition for the regularity, in both space and Malliavin sense, of strong solutions to SDEs driven by Brownian motion. We conjecture that this condition is optimal. As a consequence, we are able to improve the…

In this paper we derive a Bismut-Elworthy-Li type formula with respect to strong solutions to singular stochastic differential equations (SDE's) with additive noise given by a multi-dimensional fractional Brownian motion with Hurst…

We study the ergodicity of stochastic reaction-diffusion equation driven by subordinate Brownian motions. After establishing the strong Feller property and irreducibility of the system, we prove the tightness of the solution's law. These…

We build and study a data-driven procedure for the estimation of the stationary density f of an additive fractional SDE. To this end, we also prove some new concentrations bounds for discrete observations of such dynamics in stationary…

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…

We consider, through PDE methods, branching Brownian motion with drift and absorption. It is well know that there exists a critical drift which separates those processes which die out almost surely and those which survive with positive…