 Lp and almost sure convergence of a Milstein scheme for stochastic partial differential equationsAndrea Barth and Annika Lang Stochastic Processes and their Applications, 2013, vol. 123, issue 5, 1563-1587 Abstract: In this paper, Lp convergence and almost sure convergence of the Milstein approximation of a partial differential equation of advection–diffusion type driven by a multiplicative continuous martingale is proven. The (semidiscrete) approximation in space is a projection onto a finite dimensional function space. The considered space approximation has to have an order of convergence fitting to the order of convergence of the Milstein approximation and the regularity of the solution. The approximation of the driving noise process is realized by the truncation of the Karhunen–Loève expansion of the driving noise according to the overall order of convergence. Convergence results in Lp and almost sure convergence bounds for the semidiscrete approximation as well as for the fully discrete approximation are provided. Keywords: Stochastic partial differential equation; Lp convergence; Almost sure convergence; Milstein scheme; Galerkin method; Finite Element method; Backward Euler scheme; Advection–diffusion equation (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:123:y:2013:i:5:p:1563-1587 Ordering information: This journal article can be ordered from DOI: 10.1016/j.spa.2013.01.003 Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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