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(CMMSE2018 paper) Solving the random Pielou logistic equation with the random variable transformation technique: Theory and applications
- Source :
- Mathematical Methods in the Applied Sciences
-
Abstract
- The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples, the first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data.
- Subjects :
- education.field_of_study
Differential equation
Stochastic process
General Mathematics
Computation
010102 general mathematics
Population
General Engineering
Probability density function
01 natural sciences
010101 applied mathematics
Transformation (function)
Applied mathematics
0101 mathematics
Logistic function
education
Random variable
Mathematics
Subjects
Details
- Language :
- English
- ISSN :
- 10991476 and 01704214
- Volume :
- 42
- Issue :
- 17
- Database :
- OpenAIRE
- Journal :
- Mathematical Methods in the Applied Sciences
- Accession number :
- edsair.doi.dedup.....73a8aa54bc628f02017447b289cbedfa
- Full Text :
- https://doi.org/10.1002/mma.5440