60Jxx Markov processes
This subtopic introduces the core ideas in markov 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
60J05 Discrete-time Markov processes on general state spaces
Overview
Discrete-time Markov processes on general state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
Overview
Markov chains (discrete-time Markov processes on discrete state spaces). This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces
Overview
Applications of Markov chains and discrete-time Markov processes on general state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J22 Computational methods in Markov chains
Overview
Computational methods in Markov chains. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J25 Continuous-time Markov processes on general state spaces
Overview
Continuous-time Markov processes on general state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J27 Continuous-time Markov processes on discrete state spaces
Overview
Continuous-time Markov processes on discrete state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J28 Applications of continuous-time Markov processes on discrete state spaces
Overview
Applications of continuous-time Markov processes on discrete state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J35 Transition functions, generators and resolvents
Overview
Transition functions, generators and resolvents. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J40 Right processes
Overview
Right processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J45 Probabilistic potential theory
Overview
Probabilistic potential theory. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J46 Brownian motion on manifolds
Overview
Brownian motion on manifolds. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J50 Boundary theory
Overview
Boundary theory. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J55 Local time and additive functionals
Overview
Local time and additive functionals. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J57 Multiplicative functionals and Markov processes
Overview
Multiplicative functionals and Markov processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J60 Diffusion processes
Overview
Diffusion processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J65 Brownian motion
Overview
Brownian motion. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
Overview
Stochastic (Schramm-)Loewner evolution (SLE). This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J68 Superprocesses
Overview
Superprocesses. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J70 Applications of Brownian motions and diffusion theory
Overview
Applications of Brownian motions and diffusion theory. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J74 Jump processes on discrete state spaces
Overview
Jump processes on discrete state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J76 Jump processes on general state spaces
Overview
Jump processes on general state spaces. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J80 Branching processes
Overview
Branching processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J85 Applications of branching processes
Overview
Applications of branching processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J90 Abstract Markov processes
Overview
Abstract Markov processes. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks
60J99 None of the above
Overview
None of the above. This topic studies Markov processes, including transition structures, generators, potential theory, and long-term behavior.
Related Wikipedia Page
Wikipedia: Markov process
Useful Links
Key Ideas
- memoryless evolution and semigroups
- generators and potential kernels
- recurrence, transience, and ergodic behavior
Typical Uses
Used to model state evolution with local transition rules and analyze asymptotics via operator methods.
Applications
- Queueing and networks
- Population dynamics
- Statistical physics and Monte Carlo
References
Recommended Textbooks