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Probability theory and stochastic processes   [xref: 46T12]
{For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX}
60-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
60-01 Instructional exposition (textbooks, tutorial papers, etc.)
60-02 Research exposition (monographs, survey articles)
60-03 Historical (must also be assigned at least one classification number from Section 01)
60-04 Explicit machine computation and programs (not the theory of computation or programming)
60-06 Proceedings, conferences, collections, etc.
60-08 Computational methods (not classified at a more specific level) [See also 65C50]
60Axx Foundations of probability theory
60A05 Axioms; other general questions   [xref: 03B48]
60A10 Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}
60A99 None of the above, but in this section
60Bxx Probability theory on algebraic and topological structures   [xref: 20P05, 28A33, 46B09]
60B05 Probability measures on topological spaces
60B10 Convergence of probability measures
60B11 Probability theory on linear topological spaces [See also 28C20]   [xref: 28C20]
60B12 Limit theorems for vector-valued random variables (infinite-dimensional case)   [xref: 60Fxx]
60B15 Probability measures on groups, Fourier transforms, factorization
60B99 None of the above, but in this section
60C05 Combinatorial probability
60D05 Geometric probability, stochastic geometry, random sets [See also 52A22, 53C65]   [xref: 52A22, 53C65]
60Exx Distribution theory [See also 62Exx, 62Hxx]   [xref: 62Exx, 62Hxx]
60E05 Distributions: general theory
60E07 Infinitely divisible distributions; stable distributions
60E10 Characteristic functions; other transforms
60E15 Inequalities; stochastic orderings
60E99 None of the above, but in this section
60Fxx Limit theorems [See also 28Dxx, 60B12]   [xref: 28Dxx, 37A50]
60F05 Central limit and other weak theorems
60F10 Large deviations
60F15 Strong theorems
60F17 Functional limit theorems; invariance principles
60F20 Zero-one laws
60F25 $L^p$-limit theorems
60F99 None of the above, but in this section
60Gxx Stochastic processes   [xref: 76Fxx]
60G05 Foundations of stochastic processes
60G07 General theory of processes
60G09 Exchangeability
60G10 Stationary processes   [xref: 28Dxx, 37A50]
60G12 General second-order processes
60G15 Gaussian processes
60G17 Sample path properties
60G18 Self-similar processes
60G20 Generalized stochastic processes
60G25 Prediction theory [See also 62M20]   [xref: 62M20]
60G30 Continuity and singularity of induced measures
60G35 Applications (signal detection, filtering, etc.) [See also 62M20, 93E10, 93E11, 94Axx]   [xref: 93E10, 93E11, 94A05]
60G40 Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]   [xref: 62L15]
60G42 Martingales with discrete parameter
60G44 Martingales with continuous parameter
60G46 Martingales and classical analysis
60G48 Generalizations of martingales
60G50 Sums of independent random variables; random walks   [xref: 82B41, 82C41]
60G51 Processes with independent increments
60G52 Stable processes
60G55 Point processes
60G57 Random measures
60G60 Random fields
60G70 Extreme value theory; extremal processes
60G99 None of the above, but in this section
60Hxx Stochastic analysis [See also 58J65]   [xref: 34K50]
60H05 Stochastic integrals
60H07 Stochastic calculus of variations and the Malliavin calculus
60H10 Stochastic ordinary differential equations [See also 34F05]   [xref: 34F05, 37H10, 37L55, 58J65, 82C31]
60H15 Stochastic partial differential equations [See also 35R60]   [xref: 35R60, 37H10, 37L55]
60H20 Stochastic integral equations   [xref: 45R05]
60H25 Random operators and equations [See also 47B80]   [xref: 47B80, 47H40]
60H30 Applications of stochastic analysis (to PDE, etc.)   [xref: 76D06]
60H35 Computational methods for stochastic equations [See also 65C30]
60H40 White noise theory
60H99 None of the above, but in this section
60Jxx Markov processes   [xref: 76Fxx]
60J05 Markov processes with discrete parameter
60J10 Markov chains with discrete parameter
60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.) [See also 90B30, 91D10, 91D35, 91E40]
60J22 Computational methods in Markov chains [See also 65C40]
60J25 Markov processes with continuous parameter
60J27 Markov chains with continuous parameter
60J35 Transition functions, generators and resolvents [See also 47D03, 47D07]
60J40 Right processes
60J45 Probabilistic potential theory [See also 31Cxx, 31D05]
60J50 Boundary theory   [xref: 31C35]
60J55 Local time and additive functionals
60J57 Multiplicative functionals
60J60 Diffusion processes [See also 58J65]   [xref: 58J65, 76R50]
60J65 Brownian motion [See also 58J65]
60J70 Applications of diffusion theory (population genetics, absorption problems, etc.) [See also 92Dxx]
60J75 Jump processes
60J80 Branching processes (Galton-Watson, birth-and-death, etc.)
60J85 Applications of branching processes [See also 92Dxx]
60J99 None of the above, but in this section
60Kxx Special processes
60K05 Renewal theory
60K10 Applications (reliability, demand theory, etc.)   [xref: 90B25]
60K15 Markov renewal processes, semi-Markov processes
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]
60K25 Queueing theory [See also 68M20, 90B22]   [xref: 68M20, 90B22]
60K30 Applications (congestion, allocation, storage, traffic, etc.) [See also 90Bxx]
60K35 Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]   [xref: 82B43, 82C22, 82C43]
60K37 Processes in random environments
60K40 Other physical applications of random processes
60K99 None of the above, but in this section

Version 2000