The Markov property for generalized gaussian random fields

G. Kallianpur; V. Mandrekar

Annales de l'institut Fourier (1974)

  • Volume: 24, Issue: 2, page 143-167
  • ISSN: 0373-0956

Abstract

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We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in R n ) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.

How to cite

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Kallianpur, G., and Mandrekar, V.. "The Markov property for generalized gaussian random fields." Annales de l'institut Fourier 24.2 (1974): 143-167. <http://eudml.org/doc/74168>.

@article{Kallianpur1974,
abstract = {We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in $R^n$) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.},
author = {Kallianpur, G., Mandrekar, V.},
journal = {Annales de l'institut Fourier},
language = {eng},
number = {2},
pages = {143-167},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Markov property for generalized gaussian random fields},
url = {http://eudml.org/doc/74168},
volume = {24},
year = {1974},
}

TY - JOUR
AU - Kallianpur, G.
AU - Mandrekar, V.
TI - The Markov property for generalized gaussian random fields
JO - Annales de l'institut Fourier
PY - 1974
PB - Association des Annales de l'Institut Fourier
VL - 24
IS - 2
SP - 143
EP - 167
AB - We obtain necessary and sufficient conditions in order that a Gaussian process of many parameters (more generally, a generalized Gaussian random field in $R^n$) possess the Markov property relative to a class of open sets. The method adopted is the Hilbert space approach initiated by Cartier and Pitt. Applications are discussed.
LA - eng
UR - http://eudml.org/doc/74168
ER -

References

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  1. [1] S. AGMON, Lectures on Elliptic Boundary Value Problems, Van Nostrand, 1965. Zbl0142.37401MR31 #2504
  2. [2] P. ASSOUAD, Étude d'un espace reproduisant attaché au mouvement brownian à paramètre temporel dans Rn, C.R. Acad. Sc., Paris, 269 (1969), 36-37. Zbl0204.50702MR39 #6401
  3. [3] P. CARTIER, Introduction à l'étude des mouvements Browniens à plusieurs paramètres, Séminaire de Probabilités V, Springer-Verlag, (#191), (1971), 58-75. 
  4. [4] A. FRIEDMAN, Generalized Functions and Partial Differential Equations, Prentice-Hall, 1963. Zbl0116.07002MR29 #2672
  5. [5] H. P. MCKEAN Jr, Brownian motion with a several dimensional time, Theory Prob. Applications, 8 (1963), 335-354. Zbl0124.08702MR28 #641
  6. [6] G. M. MOLCHAN, On some problems concerning Brownian motion in Lévy's sense, Theory Prob. Applications, 12 (1967), 682-690. Zbl0159.46504
  7. [7] G. M. MOLCHAN, Characterization of Gaussian fields with Markovian property, Dokl. Akad. Nauk SSSR, 197 (1971). Translation Soviet Math. Dokl, 12 (1971), 563-567. Zbl0236.60031
  8. [8] J. PEETRE, Rectification à l'article «une caractérisation abstraite des opérateurs différentiels», Math. Scan, 8 (1960), 116-120. Zbl0097.10402MR23 #A1923
  9. [9] L. PITT, A Markov property for Gaussian processes with a multidimensional time, J. Rational Mech. and Anal, (1971), 368-391. Zbl0277.60025
  10. [10] F. TREVES, Topological Vector Spaces, Distributions and Kernels, Academic Press, 1967. Zbl0171.10402MR37 #726

Citations in EuDML Documents

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  1. Daniel Roux, Analyse multi-échelle d'un processus gaussien markovien au voisinage d'une singularité
  2. Vidyadhar Mandrekar, Germ-field Markov property for multiparameter processes
  3. Francesco Russo, Étude de la propriété de Markov étroite en relation avec les processus planaires à accroissements indépendants
  4. Albert Benassi, Processus gaussiens, markoviens d'ordre p, fortement markoviens d'ordre p et problème de Dirichlet stochastique
  5. Heinrich V. Weizsäcker, Exchanging the order of taking suprema and countable intersections of σ-algebras

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