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Projective surjectivity of quadratic stochastic operators $L_1$ and its application
- Publication Year :
- 2021
- Publisher :
- arXiv, 2021.
-
Abstract
- A nonlinear Markov chain is a discrete time stochastic process whose transitions depend on both the current state and the current distribution of the process. The nonlinear Markov chain over an infinite state space can be identified by a continuous mapping (the so-called nonlinear Markov operator) defined on a set of all probability distributions (which is a simplex). In the present paper, we consider a continuous analogue of the mentioned mapping acting on L 1 -spaces. Main aim of the current paper is to investigate projective surjectivity of quadratic stochastic operators (QSO) acting on the set of all probability measures. To prove the main result, we study the surjectivity of infinite dimensional nonlinear Markov operators and apply them to the projective surjectivity of the considered QSO. Furthermore, the obtained results are applied to the existence of the positive solution of some Hammerstein integral equations.
- Subjects :
- Simplex
Markov chain
General Mathematics
Applied Mathematics
Probability (math.PR)
General Physics and Astronomy
Discrete-time stochastic process
Statistical and Nonlinear Physics
State (functional analysis)
01 natural sciences
010305 fluids & plasmas
Functional Analysis (math.FA)
Mathematics - Functional Analysis
Nonlinear system
0103 physical sciences
FOS: Mathematics
State space
Applied mathematics
Probability distribution
010301 acoustics
Mathematics - Probability
Mathematics
Probability measure
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....f7fa5010dc53aea3ef1c3c9e5a8daf34
- Full Text :
- https://doi.org/10.48550/arxiv.2107.05290