Related papers: Regenerative processes
We replicate a renewal process at random times, which is equivalent to nesting two renewal processes, or considering a renewal process subject to stochastic resetting. We investigate the consequences on the statistical properties of the…
Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although…
Consider a single server queue with renewal arrivals and i.i.d. service times in which the server operates under a processor sharing service discipline. To describe the evolution of this system, we use a measure valued process that keeps…
We revisit processes generated by iterated random functions driven by a stationary and ergodic sequence. Such a process is called strongly stable if a random initialization exists, for which the process is stationary and ergodic, and for…
We introduce the minimal maximally predictive models ({\epsilon}-machines) of processes generated by certain hidden semi-Markov models. Their causal states are either hybrid discrete-continuous or continuous random variables and…
To unveil the logic of cell from a level of chemical reaction dynamics, we need to clarify how ensemble of chemicals can autonomously produce the set of chemical, without assuming a specific external control echanism. A cell consists of a…
Models of how things spread often assume that transmission mechanisms are fixed over time. However, social contagions--the spread of ideas, beliefs, innovations--can lose or gain in momentum as they spread: ideas can get reinforced, beliefs…
This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in…
Statistical learning relies upon data sampled from a distribution, and we usually do not care what actually generated it in the first place. From the point of view of causal modeling, the structure of each distribution is induced by…
We study a G/GI/1 single-server queuing model with i.i.d.\ service times that are independent of a stationary process of inter-arrival times. We show that the distribution of the waiting time converges to a stationary law as time tends to…
Cortical networks are strongly recurrent, and neurons have intrinsic temporal dynamics. This sets them apart from deep feed-forward networks. Despite the tremendous progress in the application of feed-forward networks and their theoretical…
Waiting times between two consecutive infection and recovery events in spreading processes are often assumed to be exponentially distributed, which results in Markovian (i.e., memoryless) continuous spreading dynamics. However, this is not…
Consider a stochastic process $\mathfrak{X}$, regenerative at a state $x$ which is instantaneous and regular. Let $L$ be a regenerative local time for $\mathfrak{X}$ at $x$. Suppose furthermore that $\mathfrak{X}$ can be approximated by…
We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control…
An overview of the recursive equations based models and their applications in simulation based analysis and optimization of queueing systems is given. These models provide a variety of systems with a convenient and unified representation in…
We employ the recently developed framework of the energetics of stochastic processes (called `stochastic energetics'), to re-analyze the Carnot cycle in detail, taking account of fluctuations, without taking the thermodynamic limit. We find…
The paper discusses a family of Markov processes that represent many particle systems, and their limiting behaviour when the number of particles go to infinity. The first part concerns model of biological systems: a model for sympatric…
Repair mechanisms are important within resilient systems to maintain the system in an operational state after an error occurred. Usually, constraints on the repair mechanisms are imposed, e.g., concerning the time or resources required…
We establish a new class of functional central limit theorems for partial sum of certain symmetric stationary infinitely divisible processes with regularly varying L\'{e}vy measures. The limit process is a new class of symmetric stable…
In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport,…