Related papers: Non-Commutative Stochastic Processes and Bi-Free P…
A probability space is a pair ($\mathcal{A},\phi $) where $\mathcal{A}$ is an algebra and $\phi $ a state on the algebra. In classical probability $\mathcal{A}$ is the algebra of linear combinations of indicator functions on the sample…
Recent developments have found unexpected connections between non-commutative probability theory and algebraic topology. In particular, Boolean cumulants functionals seem to be important for describing morphisms of homotopy operadic…
We investigate possible generalizations of the de Finetti theorem to bi-free probability. We first introduce a twisted action of the quantum permutation groups corresponding to the combinatorics of bi-freeness. We then study properties of…
It is known that non-commuting observables in quantum mechanics do not have joint probability. This statement refers to the precise (additive) probability model. I show that the joint distribution of any non-commuting pair of variables can…
We propose a direct numerical method to calculate the statistics of the number of transitions in stochastic processes, without having to resort to Monte Carlo calculations. The method is based on a generating function method, and arbitrary…
Probabilistic automata constitute a versatile and elegant model for concurrent probabilistic systems. They are equipped with a compositional theory supporting abstraction, enabled by weak probabilistic bisimulation serving as the reference…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
The outcome statistics of an informationally complete quantum measurement for a system in a given state can be used to evaluate the ensemble expectation of any linear operator in the same state, by averaging a function of the outcomes that…
Frequently, clinical trials and observational studies involve complex event history data with multiple events. When the observations are independent, the analysis of such studies can be based on standard methods for multi-state models.…
Exchangeability is a central notion in statistics and probability theory. The assumption that an infinite sequence of data points is exchangeable is at the core of Bayesian statistics. However, finite exchangeability as a statistical…
Quantum information-processing techniques enable work extraction from a system's inherently quantum features, in addition to the classical free energy it contains. Meanwhile, the science of computational mechanics affords tools for the…
The asymmetric switch process is a binary stochastic process that alternates between the values one and minus one, where the distributions of the time in these states may differ. Two versions of the process are considered: a non-stationary…
In this paper we work on (bi)simulation semantics of processes that exhibit both nondeterministic and probabilistic behaviour. We propose a probabilistic extension of the modal mu-calculus and show how to derive characteristic formulae for…
In this paper, a connection between bi-free probability and the asymptotics of random quantum channels and tensor products of random matrices is established. Using bi-free matrix models, it is demonstrated that the spectral distribution of…
We study different possibilities to apply the principles of rough paths theory in a non-commutative probability setting. First, we extend previous results obtained by Capitaine, Donati-Martin and Victoir in Lyons' original formulation of…
In this Letter, we strengthen and extend the connection between simulation and estimation to exploit simulation routines that do not exactly compute the probability of experimental data, known as the likelihood function. Rather, we provide…
In this paper we give an analytic interpretation of free convolution of type B, introduced by Biane, Goodman and Nica, and provide a new formula for its computation. This formula allows us to show that free additive convolution of type B is…
In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (non-fractional) Poisson processes. In some cases we also…
We study two-state (dichotomous, telegraph) random ergodic continuous-time processes with dynamics depending on their past. We take into account the history of process in an explicit form by introducing an integral non-local memory term…
Modeling and reasoning about concurrent quantum systems is very important both for distributed quantum computing and for quantum protocol verification. As a consequence, a general framework describing formally the communication and…