2 Young’s integrals and stochastic differential equations driven by fractional Brownian motions 4 2.1 Young’s integral and basic estimates . . . . . . . . . . . . . . . . . . 4 2.2 Stochastic differential equations driven by a Hölder path . . . . . . . 7 2.3 Multidimensional extension . . . . . . . . . . . . . . . . . . . . . . . 11 2.4 Fractional calculus . . . . . . . . . . . . . . . . . . . ...

The Calculus of Wrapped Compartments (CWC) is a variant of the Calculus of Looping Sequences (CLS). While keeping the same expressiveness, CWC strongly simplifies the development of automatic tools for the analysis of biological systems. The main simplification consists in the removal of the sequencing operator, thus lightening the formal treatment of the patterns to be matched in a term (whose...

A theory of integration for anticommuting paths is described. This is combined with standard Itô calculus to give a geometric theory of Brownian paths on curved supermanifolds. This lecture concerns a generalisation of Brownian motion and Itô calculus to include paths in spaces of anticommuting variables. The motivation for this work comes originally from physics, where anticommuting variables ...

In this study we extend stochastic-calculus allowing general probabilistic distributions to occur in its preexes. We show that no additional information is needed in the labels of transitions or in the states of systems to derive an enabling relation between transitions. Enabling is then used to compute the residual life times of parallel activities that are not immediately selected when enable...

The non-Markovian systems represent almost all stochastic processes, except of a small class having the Markov property; it is real challenge to analyze these systems. In this article, we present general method analyzing novel viewpoint given by use compact process calculus developed in formal framework computer science for describing concurrent Since phase-type distributions can approximate wi...

In this project, we work towards a continuous and spatial extension of stochastic π calculus. The continuous semantics is a useful alternative to the discrete semantics and has been recently provided for other process algebras. Ability to express spatial properties of the models is an important practical extension, specially in Systems Biology. Inspired by previous work [7][20], after showing r...

We show that iterated stochastic integrals can be described equivalently either by the conventional forward adapted, or by backward adapted quantum stochastic calculus. By using this equivalence we establish two properties of triangular (causal) and rectangular double quantum stochastic product integrals, namely a necessary and su¢ cient condition for their unitarity, and the coboundary relatio...

We consider the problem of fixed-interval smoothing of a continuous-time partially observed nonlinear stochastic dynamical system. Existing results for such smoothers require the use of two-sided stochastic calculus. The main contribution of this paper is to present a robust formulation of the smoothing equations. Under this robust formulation, the smoothing equations are nonstochastic paraboli...

In this paper we use techniques of Malliavin calculus and forward integration to present a general stochastic maximum principle for anticipating stochastic differential equations driven by a Lévy type of noise. We apply our result to study a general stochastic differential game problem of an insider. MSC2010 : 60G51, 60H40, 60H10, 60HXX, 93E20