This paper presents an abstract machine for the stochastic bioambient calculus. The abstract machine is proved sound and complete with respect to a novel stochastic semantics, and is also shown to preserve the reduction probabilities of the calculus. The machine is implemented as an extension to an existing simulator for stochastic pi-calculus.

The following notes aim to provide a very informal introduction to Stochastic Calculus, and especially to the Itô integral and some of its applications. They owe a great deal to Dan Crisan's Stochastic Calculus and Applications lectures of 1998; and also much to various books especially those of L. C. G. Rogers and D. Williams, and Dellacherie and Meyer's multi volume series 'Probabilities et P...

Langevin equation for a nano-particle suspended in a laminar fluid flow was analytically studied. The Brownian motion generated from molecular bombardment was taken as a Wiener stochastic process and approximated by a Gaussian white noise. Euler-Maruyama method was used to solve the Langevin equation numerically. The accuracy of Brownian simulation was checked by performing a series of simulati...

Abstract In this paper, we tame the uncertainty about volatility in time-averaging principle for stochastic differential equations driven by G-Brownian motion (G-SDEs) based on Lyapunov condition. That means treat condition presence of a family probability measures, each corresponding to different scenario volatility. The main tool mathematical analysis is G-stochastic calculus, which introduce...

Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the orthogonal projections of the time filtration of Fock space, together with sections of the adapted gradient operator. Free from exponential vector d...

This paper presents a stochastic fusion calculus suitable to describe systems involving general patterns of interactions. We start from fusion calculus [8] which is a symmetric generalisation of the π-calculus, and present a rate-based stochastic fusion calculus, providing a concise and compositional way to describe the behaviour of complex systems by using probability distributions. We provide...

These are lecture notes for the class Stochastic Calculus offered at the Courant Institute in the Fall Semester of 2012. It is a graduate level class. Students should have a solid background in probability and linear algebra. The topic selection is guided in part by the needs of our MS program in Mathematics in Finance. But it is not focused entirely on the Black Scholes theory of derivative pr...