- Volume 6, Number 3 (2000), 401-434.
Stochastic integral equations without probability
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.
Bernoulli, Volume 6, Number 3 (2000), 401-434.
First available in Project Euclid: 10 April 2004
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Mikosch, Thomas; Norvaiša, Rimas. Stochastic integral equations without probability. Bernoulli 6 (2000), no. 3, 401--434. https://projecteuclid.org/euclid.bj/1081616698