We present recent advances on Dirichlet forms methods either to extend financial models beyond the usual stochastic calculus or to study stochastic models with less classical tools. In this spirit, we interpret the asymptotic error on the solution of an sde due to the Euler scheme (Kurtz and Protter [Ku-Pr-91a]) in terms of a Dirichlet form on the Wiener space, what allows to propagate this err...

Wick calculus in Gaussian analysis is investigated. It is shown that this calculus can be developed in a space of regular generalized functions. The results are applied to the discussion of solutions for Wick type stochastic (partial) diierential equations. In particular, the viscous Burgers equation with a stochastic source is studied. Its solution is shown to be a regular generalized process ...

We consider -calculus, a model of concurrent processes based on the notion of naming, extended with probabilistic information. The new language is an evolution of CSP like stochastic process algebra that we call stochastic calculus. Furthermore, we integrate the semantic description of the language with topology information expressed through axioms. The new formalism is suitable to study behavi...

Stochastic differential equations in R with random coefficients are considered where one continuous driving process admits a generalized quadratic variation process. The latter and the other driving processes are assumed to possess sample paths in the fractional Sobolev space W β 2 for some β > 1/2. The stochastic integrals are determined as anticipating forward integrals. A pathwise solution p...

A variant of Rate Transition Systems (RTS), proposed by Klin and Sassone, is introduced and used as the basic model for defining stochastic behaviour of processes. The transition relation used in our variant associates to each process, for each action, the set of possible futures paired with a measure indicating their rates. We show how RTS can be used for providing the operational semantics of...

This article establishes existence and uniqueness of solutions to two classes of stochastic systems with finite memory subject to anticipating initial conditions which are sufficiently smooth in the Malliavin sense. The two classes are semilinear stochastic functional differential equations (sfdes) and fully nonlinear sfdes with a sublinear drift term. For the semilinear case, we use Malliavin ...

Abstract. The importance of identification and adaptive control of continuous-time stochastic systems are discussed. Recent developments of stochastic calculus of fractional Brownian motion and its appications to stochastic differential equations are presented. Applications of presented stochastic theory to epilepsy are shown. The educational aspects of stochastic analysis and control are discu...

This thesispresents the implementationof theCOWS2Prism system, a compiler for stochastic COWS (Calculus for Orchestration of Web Services) into Prism. The process calculus COWS is intended to aid in the precise description of Web Services compositions. This places the present informal development approach associated with Web Services into a formal reasoning framework. The COWS calculus concerns...

The following paper develops the basics behind stochastic calculus, which extends the theory of integration to stochastic (random) processes. The paper starts off with developing Brownian motion and its properties, which are used to develop the theory behind Itô integration. Several forms of the Itô integral are presented. A brief overview of the Radon-Nikodym and Girsanov Theorems are presente...