Stochastic forensics analyzes computer crime by viewing computers as stochastic processes. PDEs find their generalisation in stochastic partial differential equations. Such a sequence can be stochastic or deterministic. A crucial distinction is between deterministic and stochastic control models. A crucial distinction is between deterministic and stochastic models. Popular methods include stochastic approximation and other methods of stochastic optimization. Time series models estimate difference equations containing stochastic components. Brownian covariance is motivated by generalization of the notion of covariance to stochastic processes. Note that the noise can be either stochastic or deterministic. Thus, such matrices constitute a subset of doubly stochastic matrix. Queue theory is based on Markov chains and stochastic processes. Modelling spatial networks in respect of stochastic operations is consequent. Hilbert spaces are central to many applications, from quantum mechanics to stochastic calculus. Many improvements on the basic stochastic gradient descent algorithm have been proposed and used. There are extensions of Liouville's theorem to stochastic systems.