Stochastic integral equations without probability

T. Mikosch, R. Norvaisa

Research output: Contribution to journalArticleAcademicpeer-review

26 Citations (Scopus)
387 Downloads (Pure)

Abstract

A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0 <p <2 is the only condition on the driving stochastic process. Typical examples of such processes are infinite-variance stable Lévy motion, hyperbolic Lévy motion, normal inverse Gaussian processes, and fractional Brownian motion. The approach used in the paper is based on a chain rule for the composition of a smooth function and a function of bounded p-variation with 0 <p <2.
Original languageEnglish
Pages (from-to)401-434
JournalBernoulli
Volume6
Issue number3
DOIs
Publication statusPublished - 2000

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