On weak approximations of (a, b)-invariant diffusions
Vigirdas Mackevičius
Mathematics and Computers in Simulation (MATCOM), 2007, vol. 74, issue 1, 20-28
Abstract:
We consider scalar stochastic differential equations of the formdXt=μ(Xt)dt+σ(Xt)dBt,X0=x0,where B is a standard Brownian motion. Suppose that the coefficients are such that the solution X possesses the (a, b)-invariance property for some interval (a,b)⊂R:Xt∈(a,b) for all t≥0 if X0=x0∈(a,b). The aim of this paper is constructing weak approximations of X that preserve the above property. The main idea is splitting the equation into two equations (deterministic and stochastic parts) dX˜t=μ(X˜t)dt and X¯t=σ(X¯t)dBt. If the exact solution of one of these equations is known, we use it as the initial condition for the approximate integration of the second one. Though the idea of splitting is not new and is rather widely used for ‘domain-invariant’ strong approximations, it seems to be not yet well developed for weak approximations.
Keywords: Stochastic differential equation; Weak approximation; Euler and Milstein approximations; Split-step schemes (search for similar items in EconPapers)
Date: 2007
References: View complete reference list from CitEc
Citations:
Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475406002126
Full text for ScienceDirect subscribers only
Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
HTML/Text
Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:74:y:2007:i:1:p:20-28
DOI: 10.1016/j.matcom.2006.06.028
Access Statistics for this article
Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens
More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().