Noncommutative stochastic processes with independent and stationary increments satisfy quantum stochastic differential equations

Summary The notion of a unitary noncommutative stochastic process with independent and stationary increments is introduced, and it is proved that such a process, under a continuity assumption, can be embedded into the solution of a quantum stochastic differential equation in the sense of Hudson and Parthasarathy [8].This work was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 123, Stochastische Mathematische Modelle