Generalized stochastic processes in algebras of generalized functions: Independence, stationarity and SPDEs

Abstract

© 2019 Stochastic processes are regarded in the framework of Colombeau-type algebras of generalized functions. Colombeau stochastic processes with independent values and stationary Colombeau stochastic processes are studied with special attention paid to the property of translational invariance of generalized functions. Processes with stationary increments are characterized via stationarity of their gradient. Gaussian stationary solutions are analyzed for linear stochastic partial differential equations with generalized constant coefficients in the framework of Colombeau stochastic processes.