Related papers: Differential Equations Driven by Gaussian Signals …
We discuss stochastic calculus for large classes of Gaussian processes, based on rough path analysis. Our key condition is a covariance measure structure combined with a classical criterion due to Jain and Monrad [Ann. Probab. 11 (1983)…
In this paper, we consider a stochastic system described by a differential equation admitting a spatially varying random coefficient. The differential equation has been employed to model various static physics systems such as elastic…
In this work, we derive sufficient and necessary conditions for the existence of a weak and mild solution of an abstract stochastic Cauchy problem driven by an arbitrary cylindrical Levy process. Our approach requires to establish a…
This paper considers stochastic population dynamics driven by Levy noise. The contributions of this paper lie in that (a) Using Khasminskii-Mao theorem, we show that the stochastic differential equation associated with the model has a…
In this article we extend the framework of rough paths to processes of variable H\"older exponent or variable order paths. We show how a class of multiple discrete delay differential equations driven by signals of variable order are…
In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by L\'evy process consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are…
In the paper, we consider a type of stochastic differential equations driven by G-L\'evy processes. We prove that a kind of their additive functionals has path independence and extend some known results.
The aim of this paper is twofold. Firstly, we derive upper and lower non-Gaussian bounds for the densities of the marginal laws of the solutions to backward stochastic differential equations (BSDEs) driven by fractional Brownian motions.…
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Advances in data science are leading to new progresses in the analysis and understanding of complex dynamics for systems with experimental and observational data. With numerous physical phenomena exhibiting bursting, flights, hopping, and…
We consider a stochastic model of incompressible non-Newtonian fluids of second grade on a bounded domain of $\mathbb{R}^2$ driven by L\'evy noise. Applying the variational approach, global existence and uniqueness of strong probabilistic…
We study robust nonlinear filtering for stochastic models driven by L\'evy processes, where the signal and observation processes are coupled through common Brownian and jump noise. Robustness, defined as the continuous dependence of the…
We provide a detailed derivation of the Karhunen-Lo\`eve expansion of a stochastic process. We also discuss briefly Gaussian processes, and provide a simple numerical study for the purpose of illustration.
This article is concerned with stochastic differential equations driven by a $d$ dimensional fractional Brownian motion with Hurst parameter $H>1/4$, understood in the rough paths sense. Whenever the coefficients of the equation satisfy a…
We consider the problem of inferring a latent function in a probabilistic model of data. When dependencies of the latent function are specified by a Gaussian process and the data likelihood is complex, efficient computation often involve…
Multi-dimensional continuous local martingales, enhanced with their stochastic area process, give rise to geometric rough paths with a.s. finite homogenous p-variation, p>2. Here we go one step further and establish quantitative bounds of…
We analyze the Gaussian approximation as a method to obtain the first and second moments of a stochastic process described by a master equation. We justify the use of this approximation with ideas coming from van Kampen's expansion approach…
For many applications with multivariate data, random field models capturing departures from Gaussianity within realisations are appropriate. For this reason, we formulate a new class of multivariate non-Gaussian models based on systems of…
In this paper we consider the nonparametric functional estimation of the drift of Gaussian processes using Paley-Wiener and Karhunen-Lo\`eve expansions. We construct efficient estimators for the drift of such processes, and prove their…