We construct a new topology on the space of stopped paths and introduce calculus for causal functionals generic domains this space. propose approach to pathwise integration without any assumption variation index path obtain functional change variable formulae which extend results Föllmer [Séminaire de probabilités 15 (1981), 143–150] Cont Fournié [J. Funct. Anal. 259 (2010), no. 4, 1043–1072] l...

We make a formal analogy between random sampling and fresh name generation. show that quasi-Borel spaces, model for probabilistic programming, can soundly interpret the ν-calculus, calculus Moreover, we prove this semantics is fully abstract up to first-order types. This surprising an ‘off-the-shelf’ model, requires novel analysis of probability distributions on function spaces. Our tools are d...

Calculus via regularizations and rough paths are two methods to approach stochastic integration calculus close pathwise calculus. The origin of theory is purely deterministic, regularization based on deterministic techniques but there still a probability in the background. goal this paper establish connection between stochastically controlled-type processes, concept reminiscent from theory, so-...

the governments of the People's Republic of China and Portugal through a contribution to the UNU Endownment Fund. As well as providing two-thirds of the endownment fund, the Macau authorities also supply UNU/IIST with its ooce premises and furniture and subsidise fellow accommodation. The mission of UNU/IIST is to assist developing countries in the application and development of software techno...

We use the viewpoint of the formal calculus underlying vertex operator algebra theory to study certain aspects of the classical umbral calculus. We begin by calculating the exponential generating function of the higher derivatives of a composite function, following a very short proof which naturally arose as a motivating computation related to a certain crucial “associativity” property of an im...

A labelled transition system is presented for Milner's-calculus. This system is related to the reduction system for the calculus presented by Bellin and Scott. Also a reduction system and a labelled transition system for I-calculus are given and their correspondence is studied. This calculus is a subcalculus of-calculus in the way Sangiorgi's I-calculus is a subcalculus of ordinary-calculus.