60Gxx Stochastic processes
This subtopic introduces the core ideas in 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
60G05 Foundations of stochastic processes
Overview
Foundations of stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G07 General theory of stochastic processes
Overview
General theory of stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G09 Exchangeability for stochastic processes
Overview
Exchangeability for stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G10 Stationary stochastic processes
Overview
Stationary stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G12 General second-order stochastic processes
Overview
General second-order stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G15 Gaussian processes
Overview
Gaussian processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G17 Sample path properties
Overview
Sample path properties. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G18 Self-similar stochastic processes
Overview
Self-similar stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G20 Generalized stochastic processes
Overview
Generalized stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G22 Fractional processes, including fractional Brownian motion
Overview
Fractional processes, including fractional Brownian motion. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G25 Prediction theory
Overview
Prediction theory. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G30 Continuity and singularity of induced measures
Overview
Continuity and singularity of induced measures. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G35 Signal detection and filtering
Overview
Signal detection and filtering. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G40 Stopping times; optimal stopping problems; gambling theory
Overview
Stopping times; optimal stopping problems; gambling theory. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G42 Martingales with discrete parameter
Overview
Martingales with discrete parameter. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G44 Martingales with continuous parameter
Overview
Martingales with continuous parameter. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G46 Martingales and classical analysis
Overview
Martingales and classical analysis. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G48 Generalizations of martingales
Overview
Generalizations of martingales. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G50 Sums of independent random variables; random walks
Overview
Sums of independent random variables; random walks. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G51 Processes with independent increments; Lévy processes
Overview
Processes with independent increments; Lévy processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G52 Stable stochastic processes
Overview
Stable stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
Overview
Point processes (e.g., Poisson, Cox, Hawkes processes). This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G57 Random measures
Overview
Random measures. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G60 Random fields
Overview
Random fields. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G65 Quadratic variation processes
Overview
Quadratic variation processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G70 Extreme value theory; extremal stochastic processes
Overview
Extreme value theory; extremal stochastic processes. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks
60G99 None of the above
Overview
None of the above. This topic studies stochastic processes in continuous and discrete time, emphasizing structural properties, dependence, and path behavior.
Related Wikipedia Page
Wikipedia: Stochastic process
Useful Links
Key Ideas
- time-indexed random evolution
- sample path regularity and dependence
- distributional and functional process viewpoints
Typical Uses
Used to model random temporal phenomena and derive probabilistic structure for evolving systems.
Applications
- Signal and time-series modeling
- Finance and risk dynamics
- Queueing and reliability models
References
Recommended Textbooks