Randomly switching evolution equations
| Autor: | Marta Tyran-Kamińska, Andrzeej Tomski, Paweł Klimasara, Michael C. Mackey |
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| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Integrable system Process (engineering) Markov process 02 engineering and technology Stochastic evolution Space (mathematics) symbols.namesake 020901 industrial engineering & automation Simple (abstract algebra) 35R60 60J60 60K37 92C40 0202 electrical engineering electronic engineering information engineering FOS: Mathematics Applied mathematics Mathematics Probability (math.PR) Order (ring theory) Computer Science Applications Functional Analysis (math.FA) Mathematics - Functional Analysis Control and Systems Engineering Piecewise symbols 020201 artificial intelligence & image processing Analysis Mathematics - Probability |
| DOI: | 10.48550/arxiv.2009.04764 |
| Popis: | We present an investigation of stochastic evolution in which a family of evolution equations in L 1 are driven by continuous-time Markov processes. These are examples of so-called piecewise deterministic Markov processes (PDMP’s) on the space of integrable functions. We derive equations for the first moment and correlations (of any order) of such processes. We also introduce the mean of the process at large time and describe its behaviour. The results are illustrated by some simple, yet generic, biological examples characterized by different one-parameter types of bifurcations. |
| Databáze: | OpenAIRE |
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