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In several cases of nonlinear dispersive PDEs, the difference between the nonlinear and linear evolutions with the same initial data, i.e. the integral term in Duhamel's formula, exhibits improved regularity. This property is usually called…
We study quasi-linear stochastic partial differential equations with discontinuous drift coefficients. Existence and uniqueness of a solution is already known under weaker conditions on the drift, but we are interested in the regularity of…
A parameter estimation problem for a class of semilinear stochastic evolution equations is considered. Conditions for consistency and asymptotic normality are given in terms of growth and continuity properties of the nonlinear part.…
We study the regularity of a diffusion on a simplex with singular drift and reflecting boundary condition which describes a finite system of particles on an interval with Coulomb interaction and reflection between nearest neighbors. As our…
In this survey, we provide an in-depth exposition of our recent results on the well-posedness theory for stochastic evolution equations, employing maximal regularity techniques. The core of our approach is an abstract notion of critical…
In this article we show that a finite dimensional stochastic differential equation driven by a L\'evy process can be formulated as a stochastic partial differential equation. We prove the existence and uniqueness of strong solutions of such…
McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…
Complementing the analysis in [41], we investigate the well-posedness of SPDEs problems of doubly nonlinear type. These arise ubiquitously in the modelization of dissipative media and correspond to generalized balance laws between…
Semilinear stochastic evolution equations with multiplicative L\'evy noise and monotone nonlinear drift are considered. Unlike other similar works, we do not impose coercivity conditions on coefficients. We establish the continuous…
The main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such…
We consider a process given as the solution of a one-dimensional stochastic differential equation with irregular, path dependent and time-inhomogeneous drift coefficient and additive noise. H\"older continuity of the Lebesgue density of…
In this paper we investigate the regularity properties of strong solutions to SDEs driven by L\'evy processes with irregular drift coefficients. Under some mild conditions, we show that the singular SDE has a unique strong solution for each…
Stochastic differential equations (SDEs) are well suited to modelling noisy and irregularly sampled time series found in finance, physics, and machine learning. Traditional approaches require costly numerical solvers to sample between…
In this paper, we establish the existence and the uniqueness of solutions of stochastic evolution equations (SEEs) with reflection in an infinite dimensional ball. Our framework is sufficiently general to include e.g. the stochastic…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
Semi-linear elliptic Partial Differential Equations (PDEs) such as the non-linear Poisson Boltzmann Equation (nPBE) is highly relevant for non-linear electrostatics in computational biology and chemistry. It is of particular importance for…
In this paper, we study dimension reduction techniques for large-scale controlled stochastic differential equations (SDEs). The drift of the considered SDEs contains a polynomial term satisfying a one-sided growth condition. Such…
In this work, we consider the regularity property of stochastic convolutions for a class of abstract linear stochastic retarded functional differential equations with unbounded operator coefficients. We first establish some useful estimates…
In this paper, we investigate stochastic continuity (with respect to the initial value), irreducibility and non confluence property of the solutions of stochastic differential equations with jumps. The conditions we posed are weaker than…