Derivation of the Lindblad Generator Structure by use of the It\^o Stochastic Calculus

We use the It\^o stochastic calculus to give a simple derivation of the Lindblad form for the generator of a completely positive density matrix evolution, by specialization from the corresponding global form for a completely positive map. As a by-product, we obtain a generalized generator for a completely positive stochastic density matrix evolution.