Related papers: Hitting Times and Probabilities for Imprecise Mark…
The class of nonlinear Markov processes is characterized by the dependence of the current state of the process on its current distribution in addition to the dependence on the previous state. Due to this feature, these processes are…
Unambiguous automata are nondeterministic automata in which every word has at most one accepting run. In this paper we give a polynomial-time algorithm for model checking discrete-time Markov chains against \omega-regular specifications…
We introduce a simple approach for testing the reliability of homogeneous generators and the Markov property of the stochastic processes underlying empirical time series of credit ratings. We analyze open access data provided by Moody's and…
We explore the concept of a consistent exchangeable survival process - a joint distribution of survival times in which the risk set evolves as a continuous-time Markov process with homogeneous transition rates. We show a correspondence with…
We consider a class of discrete time Markov chains with state space [0,1] and the following dynamics. At each time step, first the direction of the next transition is chosen at random with probability depending on the current location. Then…
We propose a new abstract formalism for probabilistic timed systems, Parametric Interval Probabilistic Timed Automata, based on an extension of Parametric Timed Automata and Interval Markov Chains. In this context, we consider the…
This paper focuses on optimizing probabilities of events of interest defined over general controlled discrete-time Markov processes. It is shown that the optimization over a wide class of $\omega$-regular properties can be reduced to the…
For an ergodic Markov chain $\{X(t)\}$ on $\Bbb N$, with a stationary distribution $\pi$, let $T_n>0$ denote a hitting time for $[n]^c$, and let $X_n=X(T_n)$. Around 2005 Guy Louchard popularized a conjecture that, for $n\to \infty$, $T_n$…
We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then…
We obtain universal estimates on the convergence to equilibrium and the times of coupling for continuous time irreducible reversible finite-state Markov chains, both in the total variation and in the L^2 norms. The estimates in total…
Markov automata combine non-determinism, probabilistic branching, and exponentially distributed delays. This compositional variant of continuous-time Markov decision processes is used in reliability engineering, performance evaluation and…
Probabilistic model checking can provide formal guarantees on the behavior of stochastic models relating to a wide range of quantitative properties, such as runtime, energy consumption or cost. But decision making is typically with respect…
Computing optimal conditional reachability probabilities in Markov decision processes (MDPs) is tractable by a reduction to reachability probabilities. Yet, this reduction yields cyclic, challenging MDPs that are often notoriously hard to…
We consider the problem of approximating the reachability probabilities in Markov decision processes (MDP) with uncountable (continuous) state and action spaces. While there are algorithms that, for special classes of such MDP, provide a…
We study quantum Markov chains on graphs, described by completely positive maps, following the model due to S. Gudder (J. Math. Phys. 49, 072105, 2008) and which includes the dynamics given by open quantum random walks as defined by S.…
We consider the problem of bounding mean first passage times for a class of continuous-time Markov chains that captures stochastic interactions between groups of identical agents. The quantitative analysis of such probabilistic population…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
Markov decision processes model systems subject to nondeterministic and probabilistic uncertainty. A plethora of verification techniques addresses variations of reachability properties, such as: Is there a scheduler resolving the…
This article surveys recent advancements of strategy designs for persistent robotic surveillance tasks with the focus on stochastic approaches. The problem describes how mobile robots stochastically patrol a graph in an efficient way where…
The question of recurrence and transience of branching Markov chains is more subtle than for ordinary Markov chains; they can be classified in transience, weak recurrence, and strong recurrence. We review criteria for transience and weak…