This work highlights emergent research in the area of quantum probability. Several papers present a qualitative analysis of quantum dynamical semigroups and new results on q-deformed oscillator algebras, while others stress the application of classical stochastic processes in quantum modelling. All of the contributions have been thoroughly refereed and are an outgrowth of an international workshop in Stochastic Analysis and Mathematical Physics. The book targets an audience of mathematical physicists as well as specialists in probability theory, stochastic analysis, and operator algebras. Contributors to the volume include: R. Carbone, A.M. Chebotarev, M. Corgini, A.B. Cruzeiro, F. Fagnola, C. Fernández, J.C. García, A. Guichardet, E.B. Nielsen, R. Quezada, O. Rask, R. Rebolledo, K.B. Sinha, J.A. Van Casteren, W. von Waldenfels, L. Wu, J.C. Zambrini