Related papers: Simplified stochastic calculus via semimartingale …
In modern science, computer models are often used to understand complex phenomena, and a thriving statistical community has grown around analyzing them. This review aims to bring a spotlight to the growing prevalence of stochastic computer…
Stochastic network calculus is a newly developed theory for stochastic service guarantee analysis of computer networks. In the current stochastic network calculus literature, its fundamental models are based on the cumulative amount of…
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…
A stochastic representation for the solutions of the Poisson-Vlasov equation is obtained. The representation involves both an exponential and a branching process. The stochastic representation, besides providing an alternative existence…
In this paper, by extending the classic stochastic integrals, we investigate three kinds of more general stochastic integrals: Lebesgue-Stieltjes integrals on predictable sets of interval type (in short: PSITs), stochastic integrals on…
The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…
We consider a class of stochastic programs whose uncertain data has an exponential number of possible outcomes, where scenarios are affinely parametrized by the vertices of a tractable binary polytope. Under these conditions, we propose a…
We develop the rough path counterpart of It\^o stochastic integration and - differential equations driven by general semimartingales. This significantly enlarges the classes of (It\^o / forward) stochastic differential equations treatable…
The modelling and analysis of biological systems has deep roots in Mathematics, specifically in the field of ordinary differential equations (ODEs). Alternative approaches based on formal calculi, often derived from process algebras or term…
The syntactic nature and compositionality characteristic of stochastic process algebras make models to be easily understood by human beings, but not convenient for machines as well as people to directly carry out mathematical analysis and…
We derive a functional change of variable formula for {\it non-anticipative} functionals defined on the space of right continuous paths with left limits. The functional is only required to possess certain directional derivatives, which may…
Averaging is an important method to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. This article derives an averaged equation for a class of stochastic partial differential equations without any…
Quantum Stochastic Calculus can be used as a means by which randomness can be introduced to observables acting on a Hilbert space. In this article we show how the mechanisms of Quantum Stochastic Calculus can be used to extend the classical…
We generalise the martingale-coboundary representation of discrete time stochastic processes to the non-stationary case and to random variables in Orlicz spaces. Related limit theorems (CLT, invariance principle, log log law, probabilities…
We introduce the notion of a stochastic probabilistic program and present a reference implementation of a probabilistic programming facility supporting specification of stochastic probabilistic programs and inference in them. Stochastic…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…
Markov matrices have an important role in the filed of stochastic processes. In this paper, we will show and prove a series of conclusions on Markov matrices and transformations rather than pay attention to stochastic processes although…
The analysis of computer models can be aided by the construction of surrogate models, or emulators, that statistically model the numerical computer model. Increasingly, computer models are becoming stochastic, yielding different outputs…