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June 2000 Stochastic integral equations without probability
Thomas Mikosch, Rimas Norvaiša
Bernoulli 6(3): 401-434 (June 2000).


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.


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Thomas Mikosch. Rimas Norvaiša. "Stochastic integral equations without probability." Bernoulli 6 (3) 401 - 434, June 2000.


Published: June 2000
First available in Project Euclid: 10 April 2004

zbMATH: 0963.60060
MathSciNet: MR2001H:60100

Keywords: chain rule , extended Riemann-Stieltjes integral , fractional Brownian motion , Lévy process , p-variation , Stable process , Stochastic integral equation

Rights: Copyright © 2000 Bernoulli Society for Mathematical Statistics and Probability


Vol.6 • No. 3 • June 2000
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