scholarly journals Boundary effect in competition processes

2019 ◽  
Vol 56 (3) ◽  
pp. 750-768
Author(s):  
Vadim Shcherbakov ◽  
Stanislav Volkov
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Boundary Effect ◽  
Competitive Interaction ◽  
Continuous Time Markov Chain ◽  
Urn Models ◽  
Birth Processes ◽  
Special Case

AbstractThis paper is devoted to studying the long-term behaviour of a continuous-time Markov chain that can be interpreted as a pair of linear birth processes which evolve with a competitive interaction; as a special case, they include the famous Lotka–Volterra interaction. Another example of our process is related to urn models with ball removal. We show that, with probability one, the process eventually escapes to infinity by sticking to the boundary in a rather unusual way.

scholarly journals Calibration of Transition Intensities for a Multistate Model: Application to Long-Term Care

Risks ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 37
Author(s):  
Manuel L. Esquível ◽  
Gracinda R. Guerreiro ◽  
Matilde C. Oliveira ◽  
Pedro Corte Real
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Long Term Care ◽  
Transition Probabilities ◽  
Markov Chain Model ◽  
Chain Model ◽  
Chain Process ◽  
Term Care ◽  
National Network

We consider a non-homogeneous continuous time Markov chain model for Long-Term Care with five states: the autonomous state, three dependent states of light, moderate and severe dependence levels and the death state. For a general approach, we allow for non null intensities for all the returns from higher dependence levels to all lesser dependencies in the multi-state model. Using data from the 2015 Portuguese National Network of Continuous Care database, as the main research contribution of this paper, we propose a method to calibrate transition intensities with the one step transition probabilities estimated from data. This allows us to use non-homogeneous continuous time Markov chains for modeling Long-Term Care. We solve numerically the Kolmogorov forward differential equations in order to obtain continuous time transition probabilities. We assess the quality of the calibration using the Portuguese life expectancies. Based on reasonable monthly costs for each dependence state we compute, by Monte Carlo simulation, trajectories of the Markov chain process and derive relevant information for model validation and premium calculation.

scholarly journals Adaptive Duty Cycling in Sensor Networks With Energy Harvesting Using Continuous-Time Markov Chain and Fluid Models

2015 ◽  
Vol 33 (12) ◽  
pp. 2687-2700 ◽  
Author(s):  
Wai Hong Ronald Chan ◽  
Pengfei Zhang ◽  
Ido Nevat ◽  
Sai Ganesh Nagarajan ◽  
Alvin C. Valera ◽  
...  
Keyword(s):  
Markov Chain ◽  
Sensor Networks ◽  
Energy Harvesting ◽  
Continuous Time ◽  
Fluid Models ◽  
Continuous Time Markov Chain ◽  
Duty Cycling

STOCHASTIC MODELING OF PHYTOPLANKTON–ZOOPLANKTON INTERACTIONS WITH TOXIN PRODUCING PHYTOPLANKTON

2018 ◽  
Vol 26 (01) ◽  
pp. 87-106 ◽  
Author(s):  
T. MIHIRI M. DE SILVA ◽  
SOPHIA R.-J. JANG
Keyword(s):  
Markov Chain ◽  
Stochastic Modeling ◽  
Stochastic Models ◽  
Continuous Time ◽  
Toxin Production ◽  
Mutual Interference ◽  
Deterministic System ◽  
Continuous Time Markov Chain ◽  
Deterministic Systems ◽  
Population Interactions

We construct models of continuous-time Markov chain (CTMC) and Itô stochastic differential equations of population interactions based on a deterministic system of two phytoplankton and one zooplankton populations. The mechanisms of mutual interference among the predator zooplankton and the avoidance of toxin-producing phytoplankton (TPP) by zooplankton are incorporated. Sudden population extinctions occur in the stochastic models that cannot be captured in the deterministic systems. In addition, the effect of periodic toxin production by TPP is lessened when the birth and death of the populations are modeled randomly.

Sign in / Sign up

Export Citation Format

Share Document