Related papers: Domains and Stochastic Processes
The aim of this paper is to establish a theory of random variables on domains. Domain theory is a fundamental component of theoretical computer science, providing mathematical models of computational processes. Random variables are the…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
Two groups of naturally arising questions in the mathematical theory of domains for denotational semantics are addressed. Domains are equipped with Scott topology and represent data types. Scott continuous functions represent computable…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
We present a novel, yet rather simple construction within the traditional framework of Scott domains to provide semantics to probabilistic programming, thus obtaining a solution to a long-standing open problem in this area. Unlike current…
In this paper we present a variant of the well known Skorokhod Representation Theorem. In our main result, given $S$ a Polish space, to a given continous path $\alpha$ in the space of probability measures on $S$, we associate a continuous…
Domain theory is `a mathematical theory that serves as a foundation for the semantics of programming languages'. Domains form the basis of a theory of partial information, which extends the familiar notion of partial function to encompass a…
We give a domain-theoretic semantics to a statistical programming language, using the plain old category of dcpos, in contrast to some more sophisticated recent proposals. Remarkably, our monad of minimal valuations is commutative, which…
We present a domain-theoretic framework for probabilistic programming that provides a constructive definition of conditional probability and addresses computability challenges previously identified in the literature. We introduce a novel…
The field of statistical relational learning aims at unifying logic and probability to reason and learn from data. Perhaps the most successful paradigm in the field is probabilistic logic programming: the enabling of stochastic primitives…
Probabilistic programming is related to a compositional approach to stochastic modeling by switching from discrete to continuous time dynamics. In continuous time, an operator-algebra semantics is available in which processes proceeding in…
Classically domain theory is a rigourous mathematical structure to describe denotational semantics for programming languages and to study the computability of partial functions. Recently, the application of domain theory has also been…
The probabilistic description of the time evolution of a physical system can take two conceptually distinct forms: a trajectory of probabilities, which specifies how probabilities evolve over time, and a probability on trajectories, which…
We give an adequate denotational semantics for languages with recursive higher-order types, continuous probability distributions, and soft constraints. These are expressive languages for building Bayesian models of the kinds used in…
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first give the definition and then establish the existence of…
Stochastic network calculus is a theory for stochastic service guarantee analysis of computer communication networks. In the current stochastic network calculus literature, its traffic and server models are typically based on the cumulative…
We introduce the notion of domain-structured chaos and apply it to establish a connection between stochastic dynamics and deterministic chaos.
Many applications require stochastic processes specified on two- or higher-dimensional domains; spatial or spatial-temporal modelling, for example. In these applications it is attractive, for conceptual simplicity and computational…
Probabilistic powerdomain in domain theory plays an important role in modeling the semantics of nondeterministic functional programming languages with probabilistic choice. In this paper, we extend the notion of powerdomain to directed…
Assume that a family of stochastic processes on some Polish space $E$ converges to a deterministic process; the convergence is in distribution (hence in probability) at every fixed point in time. This assumption holds for a large family of…