The relationship of the Ito-Stratonovich stochastic calculus to studies of weakly colored noise is explained. A functional calculus approach is used to obtain an effective Fokker-Planck equation for the weakly colored noise regime. In a smooth limit, this representation produces the Stratonovich version of the ItoStratonovich calculus for white noise. It also provides an approach to steady stat...

Recently some stochastic (probabilistic) extensions of the deterministic network calculus have been developed, mainly for exploiting the statistical multiplexing of flows aggregated in packet based communication networks. This exploitation could result ”better” stochastic performance bounds than those bounds provided by the inherently worst case analysis of the deterministic network calculus. T...

Calculus via regularizations and rough paths are two methods to approach stochastic integration calculus close pathwise calculus. The origin of theory is purely deterministic, regularization based on deterministic techniques but there still a probability in the background. goal this paper establish connection between stochastically controlled-type processes, concept reminiscent from theory, so-...

We study stochastic homogenization by Γ-convergence of nonconvex integrals the calculus variations in space functions bounded deformation.

The Heston stochastic-volatility model is a square-root diffusion model for the stochasticvariance. It gives rise to a singular diffusion for the distribution as noted by Feller (1951). Hence, there is an order constraint on the relationship between the limit that the variance goes to zero and the limit that time-step goes to zero, so that any non-trivial transformation of the Heston model lead...

From the notion of stochastic Hamiltonians and the flows that they generate, we present an account of the theory of stochastic derivations over both classical and quantum algebras and demonstrate the natural way to add stochastic derivations. Our discussion on quantum stochastic processes emphasizes the origin of the Itô correction to the Leibniz rule in terms of normal ordering of white noise ...

Stochastic network calculus is a newly developed theory for stochastic ser-vice guarantee analysis of computer networks. In the current stochastic net-work calculus literature, its fundamental models are based on the cumulativeamount of traffic or cumulative amount of service. However, there are net-work scenarios where direct application of such models is difficult. This pa...

This paper describes a general approach for deriving efficient, correct abstract machines for stochastic process calculi with nested mobile compartments. The approach is applied to the Bioambient calculus and the Brane calculus. Interestingly, the abstract machines for both calculi can be defined from a common machine that supports both sets of synchronisation primitives. This illustrates the f...