Downloads & Free Reading Options - Results

Diffusion models are useful and of widespread use in many areas of control and communication theory. The models are frequently used for systems that are not quite diffusions but are, hopefully, close to a diffusion in some sense. E.g., the input noise might be 'wide-band'--but not 'white-Gaussian.' Many approximation techniques have been developed, under different sets of assumptions. The typical results are of a weak convergence nature. The physical process (x (to the epsilon power) (.)) is parameterized by the parameter epsilon, and one tries to show that (x (to the epsilon power) (.)) converges weakly to some diffusion x(.) as epsilon goes to 0. The limit process x(.) is then used to study various properties of x (to the epsilon power) (.) for small epsilon.