Stationarity in probabilistic programs
نویسنده
چکیده
We present an axiom system for a weak form of expectation operators leading to an interpretation in which a probabilistic process is modelled as a set of Markov matrices rather than a single matrix. Such`generalised Markov processes' have applications in computing science for modelling probabilistic programming and speciication languages 7, 4]. We use the resulting calculus of operators over a domain of real-valued functions to formulate and prove generalised limit theorems. In the more general context we nd that the limit theorems are considerably simpler than the corresponding results found in the probabilistic literature.
منابع مشابه
A Generalisation of Stationary Distributions, and Probabilistic Program Algebra
We generalise the classical notion of stationary distributions of Markov processes to a model of probabilistic programs which includes demonic nondeterminism. As well as removing some of the conditions normally required for stationarity, our generalisation allows the development of a complete theory linking stationary behaviour to long-term average behaviour — the latter being an important prop...
متن کاملNew verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints
In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-calle...
متن کاملOptimality Conditions for Disjunctive Programs Based on Generalized Differentiation with Application to Mathematical Programs with Equilibrium Constraints
We consider optimization problems with a disjunctive structure of the constraints. Prominent examples of such problems are mathematical programs with equilibrium constraints or vanishing constraints. Based on the concepts of directional subregularity and their characterization by means of objects from generalized differentiation, we obtain the new stationarity concept of extended M-stationarity...
متن کاملA Note on the Relation Between Strong and M-Stationarity for a Class of Mathematical Programs with Equilibrium Constraints
In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional ...
متن کاملOn Markov-switching ARMA processes – stationarity, existence of moments and geometric ergodicity
The probabilistic properties of R-valued Markov-Switching ARMA processes with a general state space parameter chain are analysed. Stationarity and ergodicity conditions are given and a feasible general stationarity condition based on a tailor-made norm is introduced. Moreover, it is shown that causality of all individual regimes is neither a necessary nor a sufficient criterion for strict negat...
متن کامل