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
  • [31] On Markov State Models for Metastable Processes
    Djurdjevac, Natasa
    Sarich, Marco
    Schuette, Christof
    PROCEEDINGS OF THE INTERNATIONAL CONGRESS OF MATHEMATICIANS, VOL IV: INVITED LECTURES, 2010, : 3105 - 3131
  • [32] State transition graph and stability of singular equilibria for piecewise linear biological models
    Wang, Jiafu
    Wang, Lin
    PHYSICA D-NONLINEAR PHENOMENA, 2013, 246 (01) : 39 - 49
  • [33] The law of the iterated logarithm for a piecewise deterministic Markov process assured by the properties of the Markov chain given by its post-jump locations
    Czapla, Dawid
    Hille, Sander C.
    Horbacz, Katarzyna
    Wojewodka-Sciazko, Hanna
    STOCHASTIC ANALYSIS AND APPLICATIONS, 2021, 39 (02) : 357 - 379
  • [34] Continuous-switch piecewise quadratic models of biological networks: Application to bacterial growth
    Carta, Alfonso
    Chaves, Madalena
    Gouze, Jean-Luc
    AUTOMATICA, 2015, 61 : 164 - 172
  • [35] On absolute continuity of invariant measures associated with a piecewise-deterministic Markov process with random switching between flows
    Czapla, Dawid
    Horbacz, Katarzyna
    Wojewodka-Sciazko, Hanna
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2021, 213
  • [36] Verifiable conditions for the irreducibility and aperiodicity of Markov chains by analyzing underlying deterministic models
    Chotard, Alexandre
    Auger, Anne
    BERNOULLI, 2019, 25 (01) : 112 - 147
  • [37] Reducing Spreading Processes on Networks to Markov Population Models
    Grossmann, Gerrit
    Bortolussi, Luca
    QUANTITATIVE EVALUATION OF SYSTEMS (QEST 2019), 2019, 11785 : 292 - 309
  • [38] Shocks models with damage effect evolutions following Markov processes
    Cui, Lirong
    Kang, Fengming
    JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY, 2023, 74 (01) : 430 - 444
  • [39] OPEN MARKOV CHAIN SCHEME MODELS FED BY SECOND ORDER STATIONARY AND NON STATIONARY PROCESSES
    Esquivel, Manuel L.
    Guerreiro, Gracinda R.
    Fernandes, Jose M.
    REVSTAT-STATISTICAL JOURNAL, 2017, 15 (02) : 277 - 297
  • [40] Thermodynamic analysis of reaction-distillation processes based on piecewise linear models
    Ryll, O.
    Blagov, S.
    Hasse, H.
    CHEMICAL ENGINEERING SCIENCE, 2014, 109 : 284 - 295
12345