Stochastic integral equations without probability

A pathwise approach to stochastic integral equations is advocated. Linear e xtended Riemann-Stieltjes integral equations driven by certain stochastic p rocesses are solved. Boundedness of the p-variation for some 0 < p < 2 is t he only condition on the driving stochastic process. Typical examples of su ch processes are infinite-variance stable Levy motion, hyperbolic Levy moti on, 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.