Within the last ten years there have been many published and unpublished contributions on how to apply Malliavin calculus in the context of mathematical finance. The purpose of this paper is on one side to give the mathematical background for the application of Malliavin calculus in the framework of the Heston stochastic volatility model, and on the other side to provide an applicable formula f...

The attributed pi calculus (π(L)) forms an extension of the pi calculus with attributed processes and attribute dependent synchronization. To ensure flexibility, the calculus is parametrized with the language L which defines possible values of attributes. π(L) can express polyadic synchronization as in pi@ and thus diverse compartment organizations. A non-deterministic and a stochastic semantic...

We introduce a natural language interface for building stochastic π calculus models of biological systems. In this language, complex constructs describing biochemical events are built from basic primitives of association, dissociation and transformation. This language thus allows us to model biochemical systems modularly by describing their dynamics in a narrative-style language, while making a...

We develop a process calculus – the nanoκ calculus – for modeling, analyzing and predicting the properties of molecular devices. The nanoκ calculus is equipped with a simple stochastic model, that we use to model and simulate the behavior of a molecular shuttle, a basic nano device currently used for building more complex systems.

We extend the Itō-to-Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Itō one and give conditions for th...