Related papers: Stochastic Partial Differential Equations on Evolv…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
We study geometric stochastic differential equations (SDEs) and their approximations on Riemannian manifolds. In particular, we introduce a simple new construction of geometric SDEs, using which with bounded curvature. In particular, we…
In this paper we develop an abstract theory for the Codazzi equation on surfaces, and use it as an analytic tool to derive new global results for surfaces in the space forms ${\bb R}^3$, ${\bb S}^3$ and ${\bb H}^3$. We give essentially…
In this note we shall introduce a simple, effective numerical method for solving partial differential equations for scalar and vector-valued data defined on surfaces. Even though we shall follow the traditional way to approximate the…
We examine the existence and uniqueness of invariant measures of a class of stochastic partial differential equations with Gaussian and Poissonian noise and its exponential convergence. This class especially includes a case of stochastic…
An averaging result is proved for stochastic evolution equations with highly oscillating coefficients. This result applies in particular to equations with almost periodic coefficients. The convergence to the solution of the averaged…
We present the random behaviour of the Schr\"odinger map equation, a geometric partial differential equation, by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results obtained are…
The concept of square-mean almost automorphy for stochastic processes is introduced. The existence and uniqueness of square-mean almost automorphic solutions to some linear and non-linear stochastic differential equations are established…
We provide a new, concise proof of weak existence and uniqueness of solutions to the stochastic differential equation for the multidimensional skew Brownian motion. We also present an application to Brownian particles with skew-elastic…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
We investigate the relation between pluri-Lagrangian hierarchies of $2$-dimensional partial differential equations and their variational symmetries. The aim is to generalize to the case of partial differential equations the recent findings…
The goal of this review article is to provide a survey about the foundations of semilinear stochastic partial differential equations. In particular, we provide a detailed study of the concepts of strong, weak and mild solutions, establish…
It is shown that, by imposing reparametrization invariance, one may derive a variety of stochastic equations describing the dynamics of surface growth and identify the physical processes responsible for the various terms. This approach…
The first part of this article develops a variational formulation for relativistic mechanics. The results are established through standard tools of variational analysis and differential geometry. The novelty here is that the main motion…
This paper is devoted to studying stochastic parabolic evolution equations with additive noise in Banach spaces of M-type 2. We construct both strict and mild solutions possessing very strong regularities. First, we consider the linear…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
In this letter we study variational obstacle avoidance problems on complete Riemannian manifolds. The problem consists of minimizing an energy functional depending on the velocity, covariant acceleration and a repulsive potential function…
In this review, we provide a concise summary of several important mathematical results for stochastic travelling waves generated by monostable and bistable reaction-diffusion stochastic partial differential equations (SPDEs). In particular,…
Statistical inference for spatial processes from partially realized or scattered data has seen voluminous developments in diverse areas ranging from environmental sciences to business and economics. Inference on the associated rates of…
We prove the existence of local stable, unstable, and center manifolds for stochastic semiflows induced by rough differential equations driven by rough paths valued stochastic processes around random fixed points of the equation. Examples…