Citation/Abstract

The Wiener process is the classical example of a mathematical model for Brownian movement. Wiener viewed Brownian movement essentially as a random walk: a Brownian particle's position at time t equals the sum of displacements over successive time intervals that partition [0, t ]. This is a guideline to the definition of integrator . We can reverse the point of view and ask the following question: Under which (minimal) conditions is the process retrievable from its increments?

We present a construction (a blueprint ) that is based on the application of multidimensional measure theory. This construction is extendible to processes indexed by n parameters.