Faculty of Economics and Business Administration Publications Database

Monotone Filterung stochastischer Prozesse

Pages: 336 - 337
Link External Source: Online Version
Year: 1985

Let X~(t) be an approximation of a stochastic process X(t) where X(t) = (FX)(t) emerges from X(t) by means of a linear filter F. If (FkX)(t) is a sequence of approximations the problem frequently occurs to guarantee lim(FkX)k→∞(t)=X(t). On condition that the filters Fk are monotone there is a criterion which enables us to decide quickly whether lim(FkX)k→∞(t)=X(t) is satisfied. Furthermore, upper bounds for the rate of convergence can be derived, and the results are applicable to interpolation and numerical integration of stochastic processes.