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 Levy motion, hyperbolic Levy 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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