Simulation and Approximation of Stochastic Processes by Spline Functions

Error bounds for simultaneous approximation of stochastic processes by means of spline functions are derived. As opposed to conventional methods, conditions such as regularity of covariances, stationarity, continuity of sample paths, etc. can be dropped, and the error bounds are valid with respect to arbitrary norms. Several applications are indicated: simulating solutions of some stochastic differential equations, computing distributions of continuous functionals by simulation as well as interpolation, numerical differentiation, and numerical integration of stochastic processes by splines.