Related papers: A Markov Process Theory for Network Growth Process…
In this work, we present a general method to establish properties of multi-dimensional continuous-time Markov chains representing stochastic reaction networks. This method consists of grouping states together (via a partition of the state…
This paper investigates tail asymptotics of stationary distributions and quasi-stationary distributions (QSDs) of continuous-time Markov chains on subsets of the non-negative integers. Based on the so-called flux-balance equation, we…
Trustless systems, such as those blockchain enpowered, provide trust in the system regardless of the trust of its participants, who may be honest or malicious. Proof-of-stake (PoS) protocols and DAG-based approaches have emerged as a better…
Consider the execution of a sequential algorithm that requires the program to converge to an optimal state, and then terminate/stutter. To design such an algorithm, we need to ensure that the state space that it traverses forms a directed…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
Mean-field models are a popular tool in a variety of fields. They provide an understanding of the impact of interactions among a large number of particles or people or other "self-interested agents", and are an increasingly popular tool in…
In this note we consider a Markov chain formed by a finite system of interacting birth-and-death processes on a finite state space. We study an asymptotic behaviour of the Markov chain as its state space becomes large. In particular, we…
Markov chain methods are remarkably successful in computational physics, machine learning, and combinatorial optimization. The cost of such methods often reduces to the mixing time, i.e., the time required to reach the steady state of the…
This paper discusses congestion control and inconsistency problems in DAG-based distributed ledgers and proposes an additional filter to mitigate these issues. Unlike traditional blockchains, DAG-based DLTs use a directed acyclic graph…
This work investigates the almost sure stabilization of a class of regime-switching systems based on discrete-time observations of both continuous and discrete components. It develops Shao's work [SIAM J. Control Optim., 55(2017), pp.…
Enumerating the directed acyclic graphs (DAGs) of a Markov equivalence class (MEC) is an important primitive in causal analysis. The central resource from the perspective of computational complexity is the delay, that is, the time an…
Inspired by a duration-dependent life insurance model, we consider continuous-time semi-Markov jump processes, initially assumed to have a finite state-space. We develop approximations using jump processes that are time-homogeneous Markov,…
Power management in multi-server data centers~especially at scale is a vital issue of increasing importance in cloud computing paradigm. Existing studies mostly consider thresholds on the number of idle servers to switch the servers on or…
DAG models are statistical models satisfying a collection of conditional independence relations encoded by the nonedges of a directed acyclic graph (DAG) $\mathcal{G}$. Such models are used to model complex cause-effect systems across a…
It is known that from purely observational data, a causal DAG is identifiable only up to its Markov equivalence class, and for many ground truth DAGs, the direction of a large portion of the edges will be remained unidentified. The golden…
Our principal aim is to observe the Markov discrete-time process of population growth with long-living trajectory. First we study asymptotical decay of generating function of Galton-Watson process for all cases as the Basic Lemma.…
In response to the bottleneck of processing throughput inherent to single chain PoW blockchains, several proposals have substituted a single chain for Directed Acyclic Graphs (DAGs). In this work, we investigate two notable DAG-oriented…
An automatic program that generates constant profit from the financial market is lucrative for every market practitioner. Recent advance in deep reinforcement learning provides a framework toward end-to-end training of such trading agent.…
In queuing theory and related problems, it is very important to know the numerical characteristics of an investigated system - both in stationary and non-stationary modes. In some cases, such characteristics can be calculated, but this is…
In this paper, the recurrent events that can occur more than one over the follow-up time have been modeled by phase-type distributions. We use the finite-state continuous-time Markov process with multi states for patients with recurrent…