Related papers: A Stochastic Reconstruction Theorem on Rectangular…
Using a Besov topology on spaces of modelled distributions in the framework of Hairer's regularity structures, we prove the reconstruction theorem on these Besov spaces with negative regularity. The Besov spaces of modelled distributions…
We study quasilinear degenerate parabolic-hyperbolic stochastic partial differential equations with general multiplicative noise within the framework of kinetic solutions. Our results are twofold: First, we establish new regularity results…
In a recent landmark paper, Khoa L\^e (2020) established a stochastic sewing lemma which since has found many applications in stochastic analysis. He further conjectured that a similar result may hold in the context of the reconstruction…
A series of recent articles introduced a method to construct stochastic partial differential equations (SPDEs) which are invariant with respect to the distribution of a given conditioned diffusion. These works are restricted to the case of…
We introduce a mixture of generalized hyperbolic distributions as an alternative to the ubiquitous mixture of Gaussian distributions as well as their near relatives of which the mixture of multivariate t and skew-t distributions are…
The reconstruction theorem and the multilevel Schauder estimate have central roles in the analytic theory of regularity structures [17]. Inspired by [26], we provide elementary proofs for them by using the semigroup of operators.…
We consider stochastic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. In particular, the diffusion term is allowed to be…
We present reduction and reconstruction procedures for the solutions of symmetric stochastic differential equations, similar to those available for ordinary differential equations. Additionally, we use the local tangent-normal…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
The main result of this paper is that there are examples of stochastic partial differential equations [hereforth, SPDEs] of the type $$ \partial_t u=\frac12\Delta u +\sigma(u)\eta \qquad\text{on $(0\,,\infty)\times\mathbb{R}^3$}$$ such that…
We study mild solutions of a class of stochastic partial differential equations, involving operators with polynomially bounded coefficients. We consider semilinear equations under suitable hyperbolicity hypotheses on the linear part. We…
In this paper a new class of generalized backward doubly stochastic differential equations is investigated. This class involves an integral with respect to an adapted continuous increasing process. A probabilistic representation for…
We introduce a new class of numerical methods for solving McKean-Vlasov stochastic differential equations, which are relevant in the context of distribution-dependent or mean-field models, under super-linear growth conditions for both the…
In this paper, we study the higher regularity theory of a mixed-type parabolic problem. We extend the recent work of \cite{DMR} to construct solutions that have an arbitrary number of derivatives in Sobolev spaces. To achieve this, we…
This paper is devoted to the study of hyperbolic systems of linear partial differential equations perturbed by a Brownian motion. The existence and uniqueness of solutions are proved by an energy method. The specific features of this class…
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…
We investigate superdiffusion for stochastic processes generated by nonuniformly hyperbolic system models, in terms of the convergence of rescaled distributions to the normal distribution following the abnormal central limit theorem, which…
Although diffusion models have successfully extended to function-valued data, stochastic interpolants -- which offer a flexible way to bridge arbitrary distributions -- remain limited to finite-dimensional settings. This work bridges this…
Systems of PDEs comprised of a combination of constraints and evolution equations are ubiquitous in physics. For both theoretical and practical reasons, such as numerical integration, it is desirable to have a systematic understanding of…