We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes. General conditions for the complete positivity of the corresponding quantum dynamical maps are formulated. The resulting non-Markovian quantum processes allow t...

Models that combine Markovian states with implicit geometric state occupancy distributions and semi-Markovian states with explicit state occupancy distributions, are investigated. This type of model retains the flexibility of hidden semi-Markov chains for the modeling of short or medium size homogeneous zones along sequences but also enables the modeling of long zones with Markovian states. The...

Previous studies have attempted to model goal scoring in sports such as ice hockey as simple Poisson processes. Others (Thomas, 2006) have shown that events within the game of ice hockey are better modelled as a Semi-Markov process determined by puck possession and location. I demonstrate that a similarly defined Semi-Markov process model is well-suited to describe the times between goals score...

Renewable energy assisted heterogeneous networks can improve system capacity and reduce conventional energy consumption. In this paper, we propose a semi-Markov decision process (SMDP)-based downlink packet scheduling scheme for solar energy assisted heterogeneous networks (HetNets), where solar radiation is modeled as a continuous-time Markov chain (CTMC) and the arrivals of multi-class downli...

Clustering of subsequences of time series is a widely studied and applied class of techniques [3, 4, 2, 6, 1, 5, 7] which aims at interpreting a time series as a shorter sequence of symbols, each of which represent a segment of the series with a pattern that is similar to other segments that has been assigned the same symbol. The research field of subsequence clustering, which was already a wid...

We study the effect of investor inertia on stock price fluctuations with a market microstructure model comprising many small investors who are inactive most of the time. It turns out that semi-Markov processes are tailor made for modelling inert investors. With a suitable scaling, we show that when the price is driven by the market imbalance, the log price process is approximated by a process w...

The previous chapter dealt with the discrete-time Markov decision model. In this model, decisions can be made only at fixed epochs t = 0, 1, . . . . However, in many stochastic control problems the times between the decision epochs are not constant but random. A possible tool for analysing such problems is the semiMarkov decision model. In Section 7.1 we discuss the basic elements of this model...

We extend first-order semi-Markov conditional random fields (semi-CRFs) to include higherorder semi-Markov features, and present efficient inference and learning algorithms, under the assumption that the higher-order semiMarkov features are sparse. We empirically demonstrate that high-order semi-CRFs outperform high-order CRFs and first-order semi-CRFs on three sequence labeling tasks with long...

Most probabilistic risk assessment (PRA) and reliability methods commonly used at Johnson Space Center (JSC) make the assumption that component failures in a system are independent random occurrences. There are some exceptions (e.g. modeling common cause events), but because of the mathematical complications that occur when full dependency is assumed, it is not done by the standard models. This...