@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://www.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://www.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://www.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://www.numdam.org/item/ASNSP_1992_4_19_2_223_0/
[1] Representation and construction of multiplicative noise, J. Funct. Anal. 87 (1989), pp. 250-272. | MR | Zbl
- - - ,[2] 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] 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] 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] 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] Global Markov Property: results and open problems, to appear in Memorial Volume for R. Høegh-Krohn, Cambridge University Press. | MR
- ,[7] The elementary Gaussian processes, Ann. Math. Statist. 15 (1944), pp. 229-282. | MR | Zbl
,[8] Markov processes and random fields, Bull. Amer. Math. Soc. 3 (1980), pp. 975-999. | MR | Zbl
,[9] VILENKIN, Generalized functions, Vol. 4 English translation, Academic Press 1964. | MR
-[10] On the Markov property for the free Euclidean electromagnetic field, Lett. Math. Phys. 4 (1980), pp. 465-467. | MR | Zbl
- ,[11] The free euclidean Proca and electromagnetic fields, Proc. International Conference Cumberland Lodge. Functional integration and its applications. 1974 Clorendon Press 1975. | MR
,[12] The Analysis of Linear Partial Differential Operators I, Springer 1983. | Zbl
,[13] Foundations of stochastic differential equations in infinite dimensional spaces, CBNS - NSF Regional Conf. Series in Appl. Math. Vol. 47 SIAM 1984. | MR | Zbl
,[14] On Linear Maps Preserving Markov Properties and Applications to Multicomponent Generalized Random Fields, Dissertation Ruhr-Universität Bochum 1990. | Zbl
,[15] On the Markov property for certain Gaussian random fields, Probab. Theory Related Fields 74 (1986), pp. 393-402. | MR | Zbl
,[16] 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] Gaussian Markov random fields, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), pp. 53-73. | MR | Zbl
,[18] Markov fields and local operators, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 26 (1979), pp. 199-212. | MR | Zbl
,[19] 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] Euclidean fields I, II and III, Publication Joint Insitute for Nuclear Research Dubna E5 12779, 12780 and 12781 (1979).
,[21] The Markov property of the free Euclidean electromagnetic field, Karl Marx Universität preprint 1982. | MR
,[22] Brownian motion with a several dimensional time, Theory Probab. Appl. 8 (1963), pp. 335-354. | MR | Zbl
,[23] The free Markov field, J. Funct. Anal. 12 (1973), pp. 211-227. | MR | Zbl
,[24] Stationary Gaussian processes with Markovian property and M. Sato's hyperfunctions, Japan. J. Math. 41 (1973), pp. 66-22. | MR | Zbl
,[25] On the germ field of stationary Gaussian processes with Markovian property, J. Math. Soc. Japan 28 (1976), pp. 86-95. | MR | Zbl
,[26] Markov properties of solutions of stochastic partial differential equations in a finite volume, Novosibirsk preprint 1989. | MR
,[27] Markov property of generalized random fields, Seventh Winter School, Czechoslovakia 1979.
- ,[28] Markov property of generalized field and axiomatic potential theory, Math. Ann. 264 (1983), pp. 153-177. | MR | Zbl
,[29] Generalized Markov Fields and Dirichlet Forms, Acta Appl. Math. 3 (1985), pp. 285-311. | MR | Zbl
,[30] Markov Randon Fields, Springer 1982. | MR | Zbl
,[31] 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] Some Functional Models for Random Fields, Chapel Hill preprint 1988.
,[33] Introduction to Fourier Analysis on Euclidean Spaces, Princeton University Press 1971. | MR | Zbl
- ,[34] On the Markov property of a class of linear infinity divisible fields, Z. Warsch. verw. Geb. 49 (1979), pp. 293-311. | MR | Zbl
,[35] On convariant stochastic differential equations and Markov property of their solutions, Istituto Fisico Università di Roma preprint 1979.
,[36] 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] Homogeneous Gauss-Markov random fields, Ann. Math. Stat. 40 (1969), pp. 1625-1634. | MR | Zbl
,[38] Stochastics Processes in Engineering Systems, Springer 1985. | MR | Zbl
- ,[39] Isotropic Gauss Markov Currents, Probab. Theory Related Fields 82 (1989), pp. 137-154. | MR | Zbl
- ,[40] 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] Measures on infinite dimensional spaces, World Scientific 1985. | MR | Zbl
,[42] Construction of quantum fields from Euclidean tensor field, J. Math. Phys. 17 (1976), pp. 241-247. | MR
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