60Kxx Special stochastic processes
This subtopic introduces the core ideas in special stochastic processes, including foundational concepts, standard methods, and the main questions used to organize the area. Typical uses include building mathematical background, framing related research problems, and supporting applications in neighboring fields where these concepts provide useful structure.
Specific topics
60K05 Renewal theory
Overview
Renewal theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K10 Applications of renewal theory
Overview
Applications of renewal theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K15 Markov renewal processes, semi-Markov processes
Overview
Markov renewal processes, semi-Markov processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K20 Applications of Markov renewal processes
Overview
Applications of Markov renewal processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K25 Queueing theory
Overview
Queueing theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K30 Applications of queueing theory
Overview
Applications of queueing theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K35 Interacting random processes; statistical mechanics type models; percolation theory
Overview
Interacting random processes; statistical mechanics type models; percolation theory. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K37 Processes in random environments
Overview
Processes in random environments. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K40 Other physical applications of random processes
Overview
Other physical applications of random processes. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K50 Anomalous diffusion models, Lévy flights
Overview
Anomalous diffusion models, Lévy flights. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks
60K99 None of the above
Overview
None of the above. This topic collects special stochastic processes such as queueing, branching, interacting particle systems, and related models.
Related Wikipedia Page
Wikipedia: Queueing theory
Useful Links
Key Ideas
- model-specific stochastic dynamics
- interacting and structured randomness
- exact and asymptotic process analysis
Typical Uses
Used for canonical stochastic models where specialized structure permits deeper analysis.
Applications
- Communication networks
- Population and epidemic modeling
- Reliability and service systems
References
Recommended Textbooks