The inverse of a local operator preserves the Markov property
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 223-253. 
@article{ASNSP_1992_4_19_2_223_0,
     author = {Iwata, Koichiro},
     title = {The inverse of a local operator preserves the {Markov} property},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {223--253},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 19},
     number = {2},
     year = {1992},
     mrnumber = {1197213},
     zbl = {0768.60044},
     language = {en},
     url = {http://archive.numdam.org/item/ASNSP_1992_4_19_2_223_0/}
}
TY  - JOUR
AU  - Iwata, Koichiro
TI  - The inverse of a local operator preserves the Markov property
JO  - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY  - 1992
SP  - 223
EP  - 253
VL  - 19
IS  - 2
PB  - Scuola normale superiore
UR  - http://archive.numdam.org/item/ASNSP_1992_4_19_2_223_0/
LA  - en
ID  - ASNSP_1992_4_19_2_223_0
ER  - 
%0 Journal Article
%A Iwata, Koichiro
%T The inverse of a local operator preserves the Markov property
%J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
%D 1992
%P 223-253
%V 19
%N 2
%I Scuola normale superiore
%U http://archive.numdam.org/item/ASNSP_1992_4_19_2_223_0/
%G en
%F ASNSP_1992_4_19_2_223_0
Iwata, Koichiro. The inverse of a local operator preserves the Markov property. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 223-253. http://archive.numdam.org/item/ASNSP_1992_4_19_2_223_0/

[1] S. Albeverio - R. Høegh-Krohn - H. Holden - T. Kolsrud, Representation and construction of multiplicative noise, J. Funct. Anal. 87 (1989), pp. 250-272. | MR | Zbl

[2] S. Albeverio - R. Høegh-Krohn - K. Iwata, Covariant markovian random fields in four space-time dimensions with nonlinear electromagnetic interaction, Proc. Dubna Conference 1987. P. Exner, P. Seba ed. Lecture Notes in Phys. 324 Springer 1989. | MR | Zbl

[3] S. Albeverio - R. Høegh-Krohn - D. Surgailis, Some Euclidean Integer-Valued Random Field with Markov Properties, Ruhr-Universität preprint 1990 to appear in Memorial Volume for R. Høegh-Krohn, Cambridge University Press. | MR | Zbl

[4] S. Albeverio - K. Iwata - T. Kolsrud, Random fields as solutions of the inhomogeneous quaternionic Cauchy-Riemann equation. I. Invariance and analytic continuation, Comm. Math. Phys. 132 (1990), pp. 555-580. | MR | Zbl

[5] S. Albeverio - K. Iwata - T. Kolsrud, Homogeneous Markov generalized vector fields and quantum fields over 4-dimensional space-time, to appear in Proc. Trento. Da Prato, Tubaro Edts. Lecture Notes in Math. Springer. | MR | Zbl

[6] S. Albeverio - B. Zegarlinski, Global Markov Property: results and open problems, to appear in Memorial Volume for R. Høegh-Krohn, Cambridge University Press. | MR

[7] J.L. Doob, The elementary Gaussian processes, Ann. Math. Statist. 15 (1944), pp. 229-282. | MR | Zbl

[8] E.B. Dynkin, Markov processes and random fields, Bull. Amer. Math. Soc. 3 (1980), pp. 975-999. | MR | Zbl

[9] I.M. Gel'Fand - N. Ya. VILENKIN, Generalized functions, Vol. 4 English translation, Academic Press 1964. | MR

[10] V. Georgescu - R. Purice, On the Markov property for the free Euclidean electromagnetic field, Lett. Math. Phys. 4 (1980), pp. 465-467. | MR | Zbl

[11] L. Gross, The free euclidean Proca and electromagnetic fields, Proc. International Conference Cumberland Lodge. Functional integration and its applications. 1974 Clorendon Press 1975. | MR

[12] L. Hörmander, The Analysis of Linear Partial Differential Operators I, Springer 1983. | Zbl

[13] K. Itô, Foundations of stochastic differential equations in infinite dimensional spaces, CBNS - NSF Regional Conf. Series in Appl. Math. Vol. 47 SIAM 1984. | MR | Zbl

[14] K. Iwata, On Linear Maps Preserving Markov Properties and Applications to Multicomponent Generalized Random Fields, Dissertation Ruhr-Universität Bochum 1990. | Zbl

[15] T. Kolsrud, On the Markov property for certain Gaussian random fields, Probab. Theory Related Fields 74 (1986), pp. 393-402. | MR | Zbl

[16] S. Kotani, On a Markov property for stationary Gaussian processes with a multidimensional parameter, Proc. 2nd Japan USSR Symposium Probability, Lecture Notes in Math. 330 Springer 1977. | MR | Zbl

[17] H. Künsch, Gaussian Markov random fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), pp. 53-73. | MR | Zbl

[18] S. Kusuoka, Markov fields and local operators, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), pp. 199-212. | MR | Zbl

[19] N. Levinson - H.P. Mckeanjr., Weighted trigonometric approximation on R1 with application to the germ field of a stationary Gaussian noise, Acta Math. 112 (1964), pp. 99-143. | MR | Zbl

[20] J. Löffelholz, Euclidean fields I, II and III, Publication Joint Insitute for Nuclear Research Dubna E5 12779, 12780 and 12781 (1979).

[21] J. Löffelholz, The Markov property of the free Euclidean electromagnetic field, Karl Marx Universität preprint 1982. | MR

[22] H.P. Mckean, Brownian motion with a several dimensional time, Theory Probab. Appl. 8 (1963), pp. 335-354. | MR | Zbl

[23] E. Nelson, The free Markov field, J. Funct. Anal. 12 (1973), pp. 211-227. | MR | Zbl

[24] Y. Okabe, Stationary Gaussian processes with Markovian property and M. Sato's hyperfunctions, Japan. J. Math. 41 (1973), pp. 66-22. | MR | Zbl

[25] Y. Okabe, On the germ field of stationary Gaussian processes with Markovian property, J. Math. Soc. Japan 28 (1976), pp. 86-95. | MR | Zbl

[26] E. Osipov, Markov properties of solutions of stochastic partial differential equations in a finite volume, Novosibirsk preprint 1989. | MR

[27] D. Preiss - R. Kotecky, Markov property of generalized random fields, Seventh Winter School, Czechoslovakia 1979.

[28] M. Röckner, Markov property of generalized field and axiomatic potential theory, Math. Ann. 264 (1983), pp. 153-177. | MR | Zbl

[29] M. Röckner, Generalized Markov Fields and Dirichlet Forms, Acta Appl. Math. 3 (1985), pp. 285-311. | MR | Zbl

[30] Yu A. Rozanov, Markov Randon Fields, Springer 1982. | MR | Zbl

[31] Yu A. Rozanov, Boundary problems for stochastic partial differential equations, Proc. BiBoS, S. Albeverio, Ph. Blanchard, L. Streit Edts., Lecture Notes in Math. 1250, Springer 1987. | MR | Zbl

[32] Yu A. Rozanov, Some Functional Models for Random Fields, Chapel Hill preprint 1988.

[33] E.M. Stein - G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press 1971. | MR | Zbl

[34] D. Surgailis, On the Markov property of a class of linear infinity divisible fields, Z. Warsch. verw. Geb. 49 (1979), pp. 293-311. | MR | Zbl

[35] D. Surgailis, On convariant stochastic differential equations and Markov property of their solutions, Istituto Fisico Università di Roma preprint 1979.

[36] H. Totoki, A method of construction of measures on function spaces and its applications to stochastic processes, Mem. Fac. Sci. Kyushu Univ. Ser. A 15 (1961), pp. 178-190. | MR | Zbl

[37] E. Wong, Homogeneous Gauss-Markov random fields, Ann. Math. Stat. 40 (1969), pp. 1625-1634. | MR | Zbl

[38] E. Wong - B. Hajek, Stochastics Processes in Engineering Systems, Springer 1985. | MR | Zbl

[39] E. Wong - M. Zakai, Isotropic Gauss Markov Currents, Probab. Theory Related Fields 82 (1989), pp. 137-154. | MR | Zbl

[40] E. Wong - M. Zakai, Spectral representation of isotropic random currents, Séminaire de Probabilités XXIII. J. Azéma, P. Meyer and M. Yor Eds. Lecture Notes in Math. 1372 Springer 1989. | Numdam | MR | Zbl

[41] Y. Yamasaki, Measures on infinite dimensional spaces, World Scientific 1985. | MR | Zbl

[42] Te Hai Yao, Construction of quantum fields from Euclidean tensor field, J. Math. Phys. 17 (1976), pp. 241-247. | MR