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PreprintarXiv licencearXiv

Quadratic Perturbations of Markov Systems

  • Riddhi Pratim Ghosh
  • Mihai D. Staic
  • Sofia Stancu
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Abstract

In this paper we study a quadratic dynamical system that is a perturbation of a system of Markov processes. We give necessary and sufficient conditions for such a perturbation to be stochastic, show the existence of fixed points, and present a few examples and possible applications. Finally, we derive explicit contraction conditions that guarantee uniqueness of the fixed point and geometric convergence to it from every initial state.

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Cite

BibTeXRIS
BibTeX
@misc{ghosh2026quadratic,
  title = {{Quadratic Perturbations of Markov Systems}},
  author = {Riddhi Pratim Ghosh and Mihai D. Staic and Sofia Stancu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.00295},
  eprint = {2608.00295},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.00295},
}
RIS
TY  - UNPB
TI  - Quadratic Perturbations of Markov Systems
AU  - Riddhi Pratim Ghosh
AU  - Mihai D. Staic
AU  - Sofia Stancu
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.00295
UR  - https://arxiv.org/abs/2608.00295
AB  - In this paper we study a quadratic dynamical system that is a perturbation of a system of Markov processes. We give necessary and sufficient conditions for such a perturbation to be stochastic, show the existence of fixed points, and present a few examples and possible applications. Finally, we derive explicit contraction conditions that guarantee uniqueness of the fixed point and geometric convergence to it from every initial state.
ER  -