Mathematics Branches, Topics, and Sub-Topics

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62Mxx Inference from stochastic processes

This subtopic introduces the core ideas in inference from 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

62M02 Markov processes: hypothesis testing

Overview

Markov processes: hypothesis testing. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M05 Markov processes: estimation

Overview

Markov processes: estimation. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M07 Non-Markovian processes: hypothesis testing

Overview

Non-Markovian processes: hypothesis testing. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M09 Non-Markovian processes: estimation

Overview

Non-Markovian processes: estimation. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M10 Time series, auto-correlation, regression, etc.

Overview

Time series, auto-correlation, regression, etc.. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M15 Inference from stochastic processes and spectral analysis

Overview

Inference from stochastic processes and spectral analysis. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M20 Inference from stochastic processes and prediction

Overview

Inference from stochastic processes and prediction. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M30 Inference from spatial processes

Overview

Inference from spatial processes. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M40 Statistics of random processes

Overview

Statistics of random processes. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks

62M45 Neural nets and related approaches to inference

Overview

Neural nets and related approaches to inference. This topic covers inference from stochastic processes, including time series, spatial processes, and dependent data models.

Related Wikipedia Page

Wikipedia: Time series

Useful Links

Key Ideas

  • dependence-aware inference
  • time/space process modeling
  • spectral and state-space methods

Typical Uses

Used to infer structure and parameters from correlated observations indexed by time or space.

Applications

  • Econometrics and forecasting
  • Environmental and geostatistical modeling
  • Signal processing and control

References

Recommended Textbooks