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Cyclic Processes

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lightbulbAbout this topic
Cyclic processes refer to a series of events or operations that repeat in a predictable sequence, often characterized by the return to an initial state after completing a cycle. These processes are fundamental in various fields, including thermodynamics, economics, and biology, where they describe systems that exhibit periodic behavior.
lightbulbAbout this topic
Cyclic processes refer to a series of events or operations that repeat in a predictable sequence, often characterized by the return to an initial state after completing a cycle. These processes are fundamental in various fields, including thermodynamics, economics, and biology, where they describe systems that exhibit periodic behavior.

Key research themes

1. How can the statistical properties and constructions of cyclic and periodic random processes be characterized and utilized for system modeling?

This research area focuses on the probabilistic characterization, construction methods, and statistical distributions of periodic and almost periodic random processes, including intrinsic location functionals and spectral densities. Understanding these properties is crucial for modeling, simulating, and evaluating systems influenced by cyclic or periodic stochastic signals, especially when departures from standard assumptions (white noise, normality) occur. Insights enable more accurate high-fidelity simulations and contribute to the analysis of systems with cyclic noise, which are prevalent in engineering, climate, and financial applications.

Key finding: Developed rigorous methods to construct finite sets of random numbers with specified amplitude distributions (normal, log-normal, Weibull, discrete) and correlations (white, pink, patchy), including nonwhite, nonnormal... Read more
Key finding: Characterized the complete convex hull of distributions achievable by intrinsic location functionals (e.g., location of path supremum, hitting times) of periodic stationary processes. Demonstrated that densities of invariant... Read more
Key finding: Developed an approach to compare and cluster spectral densities of independent almost periodically correlated (cyclostationary) processes based on asymptotic distributions of periodograms and discrete Fourier transforms.... Read more

2. How do cyclic components influence the behavior and testing of macroeconomic and business cycle time series?

This line of research investigates the presence, modeling, and analytical implications of cyclical components in economic time series—especially focusing on testing methods for unit roots in the presence of persistent cycles, and modeling of business cycles via nonlinear dynamical systems. Understanding cyclical persistence, coexistence of multiple cyclic regimes, and accurate inference in the presence of cycles has direct impact on macroeconomic forecasting, policy analysis, and the interpretation of business fluctuations.

Key finding: Provided asymptotic and finite sample results for OLS estimation and Phillips-Perron unit root tests applied to autoregressive processes containing near-integrated complex roots generating persistent cycles. Demonstrated that... Read more
Key finding: Found labor productivity at the sector level in Chilean manufacturing to be procyclical, contrasting with a-cyclical behavior at the aggregate level. Showed that heterogeneous productivity cycles across industries with... Read more
Key finding: Analyzed Goodwin's fourth (approximate) business cycle model to demonstrate coexistence of multiple limit cycles within parameter regions where the equilibrium is locally stable. Identified a stable stationary point bounded... Read more

3. What are effective probabilistic and regeneration-based methodologies for modeling, analyzing, and simulating stochastic processes with cyclical features in queueing, reliability, and dynamic system contexts?

This theme explores advanced stochastic process methods including regeneration theory for Harris recurrent Markov chains, Lindley processes in queueing and risk theory, renewal processes approximating Brownian motion, and stochastic dynamics incorporating cycles in complex systems. These methods provide frameworks to statistically analyze, simulate, and infer the behavior of systems subjected to cyclical or renewal phenomena, supporting applications in reliability engineering, financial risk, chemical dynamics, and queueing models with cyclic inputs or resets.

Key finding: Developed practical methods to identify approximate regeneration times in general Harris recurrent Markov chains using Nummelin splitting and estimated transition kernels, enabling the decomposition of observed data into... Read more
Key finding: Analyzed Lindley processes defined via recursions involving service and interarrival time distributions, connecting their finite-time distributions to renewal theory and ruin probabilities in queueing and risk models.... Read more
Key finding: Constructed families of processes from renewal reward processes generalizing uniform transport processes and showed their almost sure uniform convergence on the unit interval to standard Brownian motion, including derivation... Read more
Key finding: Developed a dynamical model of competing first-order chemical self-replicating peptides engaging in autocatalytic growth with shared nucleophile resource, demonstrating how initial stoichiometric conditions define dynamic... Read more
Key finding: Analyzed a modified telegraph process with velocity changes governed by a geometric counting process and random resets according to an independent Poisson process. Derived explicit probability laws for position and velocity,... Read more

All papers in Cyclic Processes

This paper presents the variation of radiocarbon content in annual tree rings for the period AD 1413–1553, which includes the Spoerer Minimum period (AD 1415–1534). Since the variation of the production rate of 14C is strongly related to... more
A growing number of studies on psychological phenomena employ the Ecological Momentary Assessment (EMA) method for obtaining intensive longitudinal data in daily life. Whereas cyclic processes may underlie different psychological and... more
Segmentation is an important task held to assess and analyze the heart's Right Ventricular (RV) function using CMR images. It has a major role in extracting important information which helps radiologists and doctors with the proper... more
A high-resolution cyclostratigraphic and magnetostratigraphic study was carried out on cyclically bedded successions of middle Miocene lacustrine to distal alluvial fan-floodplain deposits from the Calatayud basin, in northeast Spain.... more
A high-resolution cyclostratigraphic and magnetostratigraphic study was carried out on cyclically bedded successions of middle Miocene lacustrine to distal alluvial fan-floodplain deposits from the Calatayud basin, in northeast Spain.... more
We investigated two lignite quarries in northern Greece for orbital and suborbital 2 climate variability. Sections Lava and Vegora are located at the southern and northern 3 boundaries of the Ptolemais Basin, a northwest southeast... more
This paper presents the variation of radiocarbon content in annual tree rings for the period AD 1413–1553, which includes the Spoerer Minimum period (AD 1415–1534). Since the variation of the production rate of 14C is strongly related to... more
A growing number of studies on psychological phenomena employ the Ecological Momentary Assessment (EMA) method for obtaining intensive longitudinal data in daily life. Whereas cyclic processes may underlie different psychological and... more
A growing number of studies on psychological phenomena employ the Ecological Momentary Assessment (EMA) method for obtaining intensive longitudinal data in daily life. Whereas cyclic processes may underlie different psychological and... more
A growing number of studies on psychological phenomena employ the Ecological Momentary Assessment (EMA) method for obtaining intensive longitudinal data in daily life. Whereas cyclic processes may underlie different psychological and... more
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