Piecewise Deterministic Markov Processes in Biological Models

被引：14
|
作者：
Rudnicki, Ryszard [1 ]
Tyran-Kaminska, Marta [2 ]
机构：
[1] Polish Acad Sci, Inst Math, PL-40007 Katowice, Poland
[2] Univ Silesia, Inst Math, PL-40007 Katowice, Poland
来源：
SEMIGROUPS OF OPERATORS - THEORY AND APPLICATIONS | 2015年 / 113卷
关键词：
NEURONAL VARIABILITY; GENE-EXPRESSION; SEMIGROUPS; SYSTEMS; DENSITIES; STABILITY; EVOLUTION; FAMILIES;
D O I：
10.1007/978-3-319-12145-1_15
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to dispersal of biological systems, cell cycle models, gene expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induced by such Markov processes are applied to specific examples.
引用
收藏
页码：235 / 255
页数：21
相关论文
共 50 条
  • [41] Construction of Lyapunov Functions for Piecewise-Deterministic Markov Processes
    Mesquita, Alexandre R.
    Hespanha, Joao P.
    49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, : 2408 - 2413
  • [42] OPTIMAL CONTROL OF PARTIALLY OBSERVABLE PIECEWISE DETERMINISTIC MARKOV PROCESSES
    Bauerle, Nicole
    Lange, Dirk
    SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2018, 56 (02) : 1441 - 1462
  • [43] Quantifying and Managing Uncertainty in Piecewise-Deterministic Markov Processes
    Cartee, Elliot
    Farah, Antonio
    Nellis, April
    Van Hook, Jacob
    Vladimirsky, Alexander
    SIAM-ASA JOURNAL ON UNCERTAINTY QUANTIFICATION, 2023, 11 (03): : 814 - 847
  • [44] NONPARAMETRIC ESTIMATION FOR A CLASS OF PIECEWISE-DETERMINISTIC MARKOV PROCESSES
    Fujii, Takayuki
    JOURNAL OF APPLIED PROBABILITY, 2013, 50 (04) : 931 - 942
  • [45] Non-equilibrium Thermodynamics of Piecewise Deterministic Markov Processes
    Faggionato, A.
    Gabrielli, D.
    Crivellari, M. Ribezzi
    JOURNAL OF STATISTICAL PHYSICS, 2009, 137 (02) : 259 - 304
  • [46] STATIONARY DISTRIBUTIONS FOR PIECEWISE-DETERMINISTIC MARKOV-PROCESSES
    COSTA, OLV
    JOURNAL OF APPLIED PROBABILITY, 1990, 27 (01) : 60 - 73
  • [47] Optimal strategies for impulse control of piecewise deterministic Markov processes
    de Saporta, Benoite
    Dufour, Francois
    Geeraert, Alizee
    AUTOMATICA, 2017, 77 : 219 - 229
  • [48] Piecewise deterministic Markov processes and semi-dynamic systems
    Liu, GX
    MARKOV PROCESSES AND CONTROLLED MARKOV CHAINS, 2002, : 93 - 107
  • [49] Exponential change of measure for general piecewise deterministic Markov processes
    Zhaoyang Liu
    Yuying Liu
    Guoxin Liu
    Science China Mathematics, 2019, 62 : 719 - 734
  • [50] NUMERICAL METHOD FOR OPTIMAL STOPPING OF PIECEWISE DETERMINISTIC MARKOV PROCESSES
    de Saporta, Benoite
    Dufour, Francois
    Gonzalez, Karen
    ANNALS OF APPLIED PROBABILITY, 2010, 20 (05): : 1607 - 1637
12345