Related papers: Bisimulations for Nondeterministic Labeled Markov …
Implicit probabilistic models are models defined naturally in terms of a sampling procedure and often induces a likelihood function that cannot be expressed explicitly. We develop a simple method for estimating parameters in implicit models…
In this paper, we consider the problem of constructing a finite bisimulation quotient for a discrete-time switched linear system in a bounded subset of its state space. Given a set of observations over polytopic subsets of the state space…
Self-normalized processes are basic to many probabilistic and statistical studies. They arise naturally in the the study of stochastic integrals, martingale inequalities and limit theorems, likelihood-based methods in hypothesis testing and…
The combination of nondeterminism and probability in concurrent systems lead to the development of several interpretations of process behavior. If we restrict our attention to linear properties only, we can identify three main approaches to…
Consider an N-dimensional Markov chain obtained from N one-dimensional random walks by Doob h-transform with the q-Vandermonde determinant. We prove that as N becomes large, these Markov chains converge to an infinite-dimensional Feller…
We consider a class of sequential decision-making problems under uncertainty that can encompass various types of supervised learning concepts. These problems have a completely observed state process and a partially observed modulation…
Memoryless processes are ubiquitous in nature, in contrast with the mathematics of open systems theory, which states that non-Markovian processes should be the norm. This discrepancy is usually addressed by subjectively making the…
Even simply-defined, finite-state generators produce stochastic processes that require tracking an uncountable infinity of probabilistic features for optimal prediction. For processes generated by hidden Markov chains the consequences are…
The theory of ``Markov-up'' processes is being developed. This is a new class of stochastic processes with ``partial'' markovian features; it could also be called ``one-sided Markov''. Such a behavior may be found in the real world and in…
A recent result presented the expansion for the entropy rate of a Hidden Markov Process (HMP) as a power series in the noise variable $\eps$. The coefficients of the expansion around the noiseless ($\eps = 0$) limit were calculated up to…
We define the concept of an `open' Markov process, a continuous-time Markov chain equipped with specified boundary states through which probability can flow in and out of the system. External couplings which fix the probabilities of…
We present relaxed notions of simulation and bisimulation on Probabilistic Automata (PA), that allow some error epsilon. When epsilon is zero we retrieve the usual notions of bisimulation and simulation on PAs. We give logical…
We introduce bisimulations for the logic $ITL^e$ with `next', `until' and `release', an intuitionistic temporal logic based on structures equipped with a partial order used to interpret intuitionistic implication and a monotone function…
Labeled state-to-function transition systems, FuTS for short, admit multiple transition schemes from states to functions of finite support over general semirings. As such they constitute a convenient modeling instrument to deal with…
This paper considers discretization of the L\'evy process appearing in the Lamperti representation of a strictly positive self-similar Markov process. Limit theorems for the resulting approximation are established under some regularity…
Behavioural distances provide a quantitative approach to comparing the states of transition systems, moving beyond traditional Boolean notions of equivalence. In this paper, we develop a sound and complete axiomatisation of behavioural…
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.…
Sequential data modeling and analysis have become indispensable tools for analyzing sequential data, such as time-series data, because larger amounts of sensed event data have become available. These methods capture the sequential structure…
We present a new method of modelling numerical systems where there are two distinct output solution classes, for example tipping points or bifurcations. Gaussian process emulation is a useful tool in understanding these complex systems and…
We build on a previous statistical model for distributed systems and formulate it in a way that the deterministic and stochastic processes within the system are clearly separable. We show how internal fluctuations can be analysed in a…