Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Markov processes and random fields

Author(s): E. B. Dynkin
Journal: Bull. Amer. Math. Soc. 3 (1980), 975-999.
MSC (1980): Primary 06G60; Secondary 60G20, 60G55, 81C20
MathSciNet review: 585179
Retrieve article in: PDF

References | Similar articles | Additional information

References:

1.
P. Billingsley, Probability and measure, Wiley, New York, 1979. MR 534323
2.
R. M. Blumenthal and R. K. Getoor, Markov processes and potential theory, Academic Press, New York, 1968. MR 264757
3.
R. Cairoli and J. B. Walsh, Stochastic integrals in the plane, Acta Math. 134 (1975), 111-183. MR 420845
4.
R. L. Dobrushin and M. Ja. Kelbert, Local additive functionals of Gaussian generalized fields, Uspehi Mat. Nauk 34 (1979), No. 5, 223-224. (Russian) MR 562804
5.
E. B. Dynkin, Theory of Markov processes, Pergamon Press, Oxford, 1960. MR 131900
6.
E. B. Dynkin, Markov processes, Vols. I and II, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. MR 193671
7.
E. B. Dynkin, Markov processes. Theorems and problems, Plenum, New York, 1969. MR 242252
8.
E. B. Dynkin, Regular Markov processes, Uspehi Mat. Nauk 28 (1973), No. 2, 35-64. (English translation: Russian Math. Surveys 28, (1973), No. 2, 33-64) MR 400410
9.
E. B. Dynkin, Markov systems and their additive functionals, Ann. Probability 5 (1977), 653-677. MR 451415
10.
E. B. Dynkin, Additive functionals of non-interacting Markov processes (in preparation).
11.
M. Fukushima, Dirichlet forms and Markov processes, North-Holland, Amsterdam, Oxford, New York, 1980. Kodashira, Tokyo. MR 569058
12.
R. K. Getoor, Markov processes: Ray processes and right processes, Lecture Notes in Math., vol. 440, Springer-Verlag, Berlin and New York, 1975. MR 405598
13.
M. Hall, Jr., Combinatorial theory, Blaisdell, Waltham, Mass., 1967. MR 224481
14.
E. Hille, Functional analysis and semigroups, New York, 1948.
15.
K. Ito, Multiple Wiener integral, J. Math. Soc. Japan 3 (1951), 157-169. MR 44064
16.
S. Kakutani, Determination of the spectrum of the flow of Brownian motion, Proc. Nat. Acad. Sci. U.S.A. 36 (1950), 319-323. MR 35924
17.
S. Karlin and H. M. Taylor, A first course in stochastic processes, 2nd ed., Academic Press, New York, 1975. MR 356197
18.
H. McKean, Brownian motion with a several-dimensional time, Teor. Verojatnost. i Primenen. 8 (1963), 357-378 = Theor. Probability Appl. 3 (1963), 335-354. MR 157407
19.
P. A. Meyer, Probability and potentials, Blaisdell, Waltham, Mass., 1966. MR 205288
20.
G. M. Molchan, Characterization of Gaussian fields with Markovian property, Dokl. Acad. Nauk SSSR 197 (1971), No. 4, 784-787. (English translation: Soviet Math. Dokl. 12 (1971), No. 2, 563-567) MR 297018
21.
G. M. Molchan, L-Markov Gaussian fields, Dokl. Acad. Nauk SSSR 215 (1974), No. 5, 1054-1057. (English translation: Soviet Math. Dokl. 15 (1974), No. 2, 657-662) MR 368124
22.
E. Nelson, Construction of quantum fields from Markov fields, J. Functional Analysis 12 (1973), 97-112. MR 343815
23.
E. Nelson, The free Markov field, J. Functional Analysis 12 (1973), 211-227. MR 343816
24.
J. Neveu, Processus aléatoires Gaussiens, Les Presses de l'Université de Montréal, Montréal, 1968. MR 272042
25.
S. Orey and W. Pruitt, Sample functions of the N-parameter Wiener process, Ann. Probability 1 (1973), 138-163. MR 346925
26.
I. Segal, Tensor algebras over Hilbert spaces. I, Trans. Amer. Math. Soc. 81 (1956), 106-134. MR 76317
27.
M. L. Silverstein, Symmetric Markov processes, Lecture Notes in Math., vol. 426, Springer-Verlag, Berlin, Heidelberg, New York, 1974. MR 386032
28.
B. Simon, The P(Φ)2 Euclidean (quantum) field theory, Princeton Univ. Press, Princeton, N. J., 1974. MR 489552
29.
J. B. Walsh, Martingales with a multi-dimensional parameter and stochastic integrals in the plane, Lecture Notes, Université P.&M. Curie, Paris, 1976/1977.
30.
R. L. Wolpert, Wiener path intersections and local time, J. Functional Analysis 30 (1978), 329-340. MR 518339
31.
R. L. Wolpert, Local time and a particle picture for Euclidean field theory, J. Functional Analysis 30 (1978), 341-357. MR 518340
32.
R. L. Wolpert, The prediction problem for the Wiener-Yeh process (in preparation).
33.
E. Wong and M. Zakai, Martingales and stochastic integrals for processes with a multi-dimensional parameter, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 29 (1974), 109-122. MR 370758
34.
J. Yen, Wiener measure in a space of functions of two variables, Trans. Amer. Math. Soc. 95 (1960), 433-450. MR 125433

Similar Articles:

Retrieve articles in Bulletin of the American Mathematical Society with MSC (1980): 06G60, 60G20, 60G55, 81C20

Retrieve articles in all Journals with MSC (1980): 06G60, 60G20, 60G55, 81C20


Additional Information:

DOI: 10.1090/S0273-0979-1980-14831-4
PII: S 0273-0979(1980)14831-4




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia