A representation for self-similar processes

摘要: Abstract A self-similar process Z(t) has stationary increments and is invariant in law under the transformation Z(i)→c-HZ(ct), c⩾0. The choice 1 2 ensures that of exhibit a long range positive correlation. Mandelbrot Van Ness investigated case where Gaussian represented as fractional integral Brownian motion. They called it This paper provides time-indexed representation for sequence self- similar processes Z m (t) , m=1,2,…, whose finite-dimensional moments have been specified an earlier paper. motion but are not when m⩾2. Self-similar being studied physics, context renormalization group theory critical phenomena, hydrology they account so-called “Hurst effect”.