ABSTRACT
Initial-boundary value problems (IBVPs) involve differential equations whose terms
describe certain features (physical, chemical, biological, etc.) of the phenomenon un-
der investigation, as well as initial and boundary conditions that are often determined
experimentally. The experiments that yield these parameters or conditions are con-
ducted repeatedly and produce slightly different outcomes due to underlying noise.
In deterministic settings, an average of these values is often used as an approximation
to the parameter. Doing so effectively removes randomness from the IBVP. Such IB-
VPs were studied in Volume 1 [295]. The goal of this text is to develop an analogous
abstract theory that enables us to study IBVPs without removing randomness from
the model.
