Fractal Dimension of Random Processes

The fractal dimension problem of random processes with almost certain continuous realizations is solved. It is shown that the fractal properties of such processes are completely defined by the behaviour of their covariance functions, K(t1,t2), in a small vicinity of the point t1 = t2. The fractal dimension of diffusive Markovian processes and generalized Wiener processes is calculated and the connection of the diffusion character of particles ensemble with fractal dimension of their coordinates is established.