The material presented here is covered in the books by Neftci (An Introduction to the Mathematics of Financial Derivatives), or Chang (Stochastic Optimization in Continuous Time). Deeper treatments can be found for example in Shreve (Stochastic Calculus for Finance II), Steele (Stochastic Calculus and Financial Applications), and Oksendal (Stochastic Differential Equations: an Introduction with...

A stochastic calculus similar to Malliavin’s calculus is worked out for Brownian excursions. The analogue of the Malliavin derivative in this calculus is not a differential operator, but its adjoint is (like the Skorohod integral) an extension of the Itô integral. As an application, we obtain an expression for the integrand in the stochastic integral representation of square integrable Wiener f...

We describe a novel application of a stochastic name-passing calculus for the study of biomolecular systems. We specify the structure and dynamics of biochemical networks in a variant of the stochastic π-calculus, yielding a model which is mathematically well-defined and biologically faithful. We adapt the operational semantics of the calculus to account for both the time and probability of bio...

Network calculus is a powerful methodology of characterizing queueing processes and has wide applications, but few works on applying it to 802.11 by far. In this paper, we take one of the first steps to analyze the backlog bounds of an 802.11 wireless LAN using stochastic network calculus. In particular, we want to address its effectiveness on bounding backlogs. We model a wireless node as a si...