THE QUADRATIC VARIATION OF RANDOM PROCESSES,

A study is presented of the quadratic variation of the sample functions of random processes having finite fourth moments. The quadratic variation of a function is related to the regular variation and is thus an indicator of the smoothness of the function. Conditions on the fourth moments of the random process are presented which ensure that the quadratic variation is finite and non-zero. In addition the concept of the quadratic variation is generalized to general quadratic functionals of the increments of a random process. These functionals are used to show the relationship between the quadratic variation and the Fourier coefficients of certain random processes. Author