Search results for "stochastic partial differential equation"
showing 8 items of 38 documents
On ordinary differential equations with interface conditions
1968
Adaptive Wavelet Methods for SPDEs
2014
We review a series of results that have been obtained in the context of the DFG-SPP 1324 project “Adaptive wavelet methods for SPDEs”. This project has been concerned with the construction and analysis of adaptive wavelet methods for second order parabolic stochastic partial differential equations on bounded, possibly nonsmooth domains \(\mathcal{O}\subset \mathbb{R}^{d}\). A detailed regularity analysis for the solution process u in the scale of Besov spaces \(B_{\tau,\tau }^{s}(\mathcal{O})\), 1∕τ = s∕d + 1∕p, α > 0, p ≥ 2, is presented. The regularity in this scale is known to determine the order of convergence that can be achieved by adaptive wavelet algorithms and other nonlinear appro…
Hydrodynamics and Stochastic Differential Equation with Sobolev Coefficients
2013
In this chapter, we will explain how the Brenier’s relaxed variational principle for Euler equation makes involved the ordinary differential equations with Sobolev coefficients and how the investigation on stochastic differential equations (SDE) with Sobolev coefficients is useful to establish variational principles for Navier–Stokes equations. We will survey recent results on this topic.
Linear Systems Excited by Polynomials of Filtered Poission Pulses
1997
The stochastic differential equations for quasi-linear systems excited by parametric non-normal Poisson white noise are derived. Then it is shown that the class of memoryless transformation of filtered non-normal delta correlated process can be reduced, by means of some transformation, to quasi-linear systems. The latter, being excited by parametric excitations, are frst converted into ltoˆ stochastic differential equations, by adding the hierarchy of corrective terms which account for the nonnormality of the input, then by applying the Itoˆ differential rule, the moment equations have been derived. It is shown that the moment equations constitute a linear finite set of differential equatio…
Set-valued and fuzzy stochastic differential equations driven by semimartingales
2013
Abstract In the paper we present set-valued and fuzzy stochastic integrals with respect to semimartingale integrators as well as their main properties. Then we study the existence of solutions to set-valued and fuzzy-set-valued stochastic differential equations driven by semimartingales. The stability of solutions is also established.
Spatial Bayesian Modeling Applied to the Surveys of Xylella fastidiosa in Alicante (Spain) and Apulia (Italy)
2020
The plant-pathogenic bacterium Xylella fastidiosa was first reported in Europe in 2013, in the province of Lecce, Italy, where extensive areas were affected by the olive quick decline syndrome, caused by the subsp. pauca. In Alicante, Spain, almond leaf scorch, caused by X. fastidiosa subsp. multiplex, was detected in 2017. The effects of climatic and spatial factors on the geographic distribution of X. fastidiosa in these two infested regions in Europe were studied. The presence/absence data of X. fastidiosa in the official surveys were analyzed using Bayesian hierarchical models through the integrated nested Laplace approximation (INLA) methodology. Climatic covariates were obtained from …
Modeling the Spatial Distribution of Xylella fastidiosa: A Nonstationary Approach with Dispersal Barriers
2022
Spatial species distribution models often assume isotropy and stationarity, implying that spatial dependence is direction-invariant and uniform throughout the study area. However, these assumptions are violated when dispersal barriers are present. Despite this, the issue of nonstationarity has been little explored in the context of plant health. The objective of this study was to evaluate the influence of barriers in the distribution of Xylella fastidiosa in the demarcated area in Alicante, Spain. Occurrence data from 2018 were analyzed through spatial Bayesian hierarchical models. The stationary model, illustrating a scenario without control interventions or geographical features, was com…
Opinion dynamics and stubbornness through mean-field games
2013
This paper provides a mean field game theoretic interpretation of opinion dynamics and stubbornness. The model describes a crowd-seeking homogeneous population of agents, under the influence of one stubborn agent. The game takes on the form of two partial differential equations, the Hamilton-Jacobi-Bellman equation and the Kolmogorov-Fokker-Planck equation for the individual optimal response and the population evolution, respectively. For the game of interest, we establish a mean field equilibrium where all agents reach epsilon-consensus in a neighborhood of the stubborn agent's opinion.