# AbstractsMathematics

by Elin Engen Røse

Institution: University of Oslo 1000 VDP::410 1290712 https://www.duo.uio.no/handle/10852/10158https://www.duo.uio.no/bitstream/10852/10158/1/MasteroppgaveElinERose.pdf

## Abstract

We regard a stochastic process as a weakly measurable function, taking values one of the Kondratiev Stochastic distribution spaces, (S)_{-\rho}. Since these spaces are duals of nuclear spaces, functions taking values in the dual of a nuclear space are treated in detail. The space (S)_{-1} is a topological algebra with respect to the Wick product, ⋄, and the following relation hold, ∫Y(s)δη(s)=∫Y(s)⋄\dot{η}(s)ds. As a consequence, we can regard SDEs as (S)_{-1}-valued ODEs. Similarily, we will regard an SPDE as an (S)_{-1}-valued PDE.