Mathematics Subject Classification 1991

60-XX Probability theory and stochastic processes, {For additional applications, See 11Kxx, 62-XX, 90-XX, 92-XX, 93-XX, 94-XX. For numerical results, See 65U05} ( 0 Dok.)

• 60-00 General reference works (handbooks, dictionaries, bibliographies, etc.) ( 0 Dok.)
• 60-01 Instructional exposition (textbooks, tutorial papers, etc.) ( 0 Dok.)
• 60-02 Research exposition (monographs, survey articles) ( 0 Dok.)
• 60-03 Historical (must be assigned at least one classification number from Section 01) ( 0 Dok.)
• 60-04 Explicit machine computation and programs (not the theory of computation or programming) ( 0 Dok.)
• 60-06 Proceedings, conferences, collections, etc. ( 0 Dok.)
• 60Axx Foundations of probability theory ( 0 Dok. )
• 60A05 Axioms; other general questions ( 0 Dok.)
• 60A10 Probabilistic measure theory, {For ergodic theory, See 28Dxx and 60Fxx} ( 0 Dok.)
• 60A99 None of the above but in this section ( 0 Dok.)
• 60Bxx Probability theory on algebraic and topological structures ( 0 Dok. )
• 60B05 Probability measures on topological spaces ( 0 Dok.)
• 60B10 Convergence of probability measures ( 0 Dok.)
• 60B11 Probability theory on linear topological spaces, See Also { 28C20} ( 0 Dok.)
• 60B12 Limit theorems for vector-valued random variables (infinite-dimensional case) ( 0 Dok.)
• 60B15 Probability measures on groups, Fourier transforms, factorization ( 0 Dok.)
• 60B99 None of the above but in this section ( 0 Dok.)
• 60C05 Combinatorial probability ( 0 Dok.)
• 60D05 Geometric probability, stochastic geometry, random sets, See also {52A22, 53C65} ( 0 Dok.)
• 60Exx Distribution theory, See also {62Exx, 62Hxx} ( 0 Dok. )
• 60E05 Distributions: general theory ( 0 Dok.)
• 60E07 Infinitely divisible distributions; stable distributions ( 0 Dok.)
• 60E10 Characteristic functions; other transforms ( 0 Dok.)
• 60E15 Inequalities (Chebyshev, Kolmogorov, etc.) ( 0 Dok.)
• 60E99 None of the above but in this section ( 0 Dok.)
• 60Fxx Limit theorems, See also {28Dxx, 60B12} ( 0 Dok. )
• 60F05 Central limit and other weak theorems ( 0 Dok.)
• 60F10 Large deviations ( 0 Dok.)
• 60F15 Strong theorems ( 0 Dok.)
• 60F17 Functional limit theorems; invariance principles ( 0 Dok.)
• 60F20 Zero-one laws ( 0 Dok.)
• 60F25 $L^p$-limit theorems ( 0 Dok.)
• 60F99 None of the above but in this section ( 0 Dok.)
• 60Gxx Stochastic processes ( 0 Dok. )
• 60G05 Foundations of stochastic processes ( 0 Dok.)
• 60G07 General theory of processes ( 0 Dok.)
• 60G09 Exchangeability ( 0 Dok.)
• 60G10 Stationary processes ( 0 Dok.)
• 60G12 General second-order processes ( 0 Dok.)
• 60G15 Gaussian processes ( 0 Dok.)
• 60G17 Sample path properties ( 0 Dok.)
• 60G18 Self-similar processes ( 0 Dok.)
• 60G20 Generalized stochastic processes ( 0 Dok.)
• 60G25 Prediction theory, See also {62M20} ( 0 Dok.)
• 60G30 Continuity and singularity of induced measures ( 0 Dok.)
• 60G35 Applications (signal detection, filtering, etc.), See Also { 62M20, 93E10, 93E11, 94Axx} ( 0 Dok.)
• 60G40 Stopping times; optimal stopping problems; gambling theory, See also {62L15, 90D60} ( 0 Dok.)
• 60G42 Martingales with discrete parameter ( 0 Dok.)
• 60G44 Martingales with continuous parameter ( 0 Dok.)
• 60G46 Martingales and classical analysis ( 0 Dok.)
• 60G48 Generalizations of martingales ( 0 Dok.)
• 60G50 Sums of independent random variables ( 0 Dok.)
• 60G55 Point processes ( 0 Dok.)
• 60G57 Random measures ( 0 Dok.)
• 60G60 Random fields ( 0 Dok.)
• 60G70 Extreme value theory; extremal processes ( 0 Dok.)
• 60G99 None of the above but in this section ( 0 Dok.)
• 60Hxx Stochastic analysis, See also {58G32} ( 0 Dok. )
• 60H05 Stochastic integrals ( 0 Dok.)
• 60H07 Stochastic calculus of variations and the Malliavin calculus ( 0 Dok.)
• 60H10 Stochastic ordinary differential equations, See Also { 34F05} ( 0 Dok.)
• 60H15 Stochastic partial differential equations, See also {35R60} ( 0 Dok.)
• 60H20 Stochastic integral equations ( 0 Dok.)
• 60H25 Random operators and equations, See also {47B80} ( 0 Dok.)
• 60H30 Applications of stochastic analysis (to PDE, etc.) ( 0 Dok.)
• 60H99 None of the above but in this section ( 0 Dok.)
• 60Jxx Markov processes ( 0 Dok. )
• 60J05 Markov processes with discrete parameter ( 0 Dok.)
• 60J10 Markov chains with discrete parameter ( 0 Dok.)
• 60J15 Random walks ( 0 Dok.)
• 60J20 Applications of discrete Markov processes (social mobility, learning theory, industrial processes, etc.), See Also { 90B30, 92H10, 92H35, 92J40} ( 0 Dok.)
• 60J25 Markov processes with continuous parameter ( 0 Dok.)
• 60J27 Markov chains with continuous parameter ( 0 Dok.)
• 60J30 Processes with independent increments ( 0 Dok.)
• 60J35 Transition functions, generators and resolvents, See Also { 47D03, 47D07} ( 0 Dok.)
• 60J40 Right processes ( 0 Dok.)
• 60J45 Probabilistic potential theory, See also {31Cxx, 31D05} ( 0 Dok.)
• 60J50 Boundary theory ( 0 Dok.)
• 60J55 Local time and additive functionals ( 0 Dok.)
• 60J57 Multiplicative functionals ( 0 Dok.)
• 60J60 Diffusion processes, See also {58G32} ( 0 Dok.)
• 60J65 Brownian motion, See also {58G32} ( 0 Dok.)
• 60J70 Applications of diffusion theory (population genetics, absorption problems, etc.), See also {92Dxx} ( 0 Dok.)
• 60J75 Jump processes ( 0 Dok.)
• 60J80 Branching processes (Galton-Watson, birth-and-death, etc.) ( 0 Dok.)
• 60J85 Applications of branching processes, See also {92Dxx} ( 0 Dok.)
• 60J99 None of the above but in this section ( 0 Dok.)
• 60Kxx Special processes ( 0 Dok. )
• 60K05 Renewal theory ( 0 Dok.)
• 60K10 Applications (reliability, demand theory, etc.) ( 0 Dok.)
• 60K15 Markov renewal processes, semi-Markov processes ( 0 Dok.)
• 60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.), See also {90Bxx} ( 0 Dok.)
• 60K25 Queueing theory, See also {68M20, 90B22} ( 0 Dok.)
• 60K30 Applications (congestion, allocation, storage, traffic, etc.), See also {90Bxx} ( 0 Dok.)
• 60K35 Interacting random processes; statistical mechanics type models; percolation theory, See also {82B43, 82C43} ( 0 Dok.)
• 60K40 Other physical applications of random processes ( 0 Dok.)
• 60K99 None of the above but in this section ( 0 Dok.)