publication . Book . 2016

The one-way Fubini property and conditional independence : an equivalence result

Hammond, Peter J.; Sun, Yeneng;
Open Access English
  • Published: 01 Apr 2016
  • Publisher: University of Warwick. Department of Economics
  • Country: United Kingdom
Abstract
A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a countably generated σ-algebra given which the random variables are essentially pairwise conditionally independent, while their joint conditional distribution also satisfies a suitable joint measurability condition. Applications include new characterizations of essential pairwis...
Subjects
free text keywords: QA
Related Organizations
22 references, page 1 of 2

[4] P. Billingsley, Probability and Measure, 3rd. edn., Wiley, New York, 1995.

[5] D. L. Cohn, Measure Theory, Birkhauser, Boston, 1980.

[6] J. L. Doob, Stochastic processes depending on a continuous parameter, Transactions of the American Mathematical Society 42 (1937), 107{140. [OpenAIRE]

[7] J. L. Doob, Stochastic Processes, Wiley, New York, 1953.

[8] R. M. Dudley, Real Analysis and Probability, Chapman & Hall, New York, 1989.

[9] R. Durrett, Probability: Theory and Examples, Wadsworth, Belmont, California, 1991.

[10] P. J. Hammond and Y. N. Sun, Monte Carlo simulation of macroeconomic risk with a continuum of agents: The symmetric case, Economic Theory 21 (2003), 743{766.

[11] P. J. Hammond and Y. N. Sun, Joint measurability and the one-way Fubini property for a continuum of independent random variables, Proceedings of the American Mathematical Society 134 (2006), 737{747.

[12] P. J. Hammond and Y. N. Sun, The essential equivalence of pairwise and mutual conditional independence, Probability Theory and Related Fields 135 (2006), 415{427.

[13] P. J. Hammond and Y. N. Sun, Monte Carlo simulation of macroeconomic risk with a continuum of agents: The general case, Economic Theory 36 (2008), 303{325.

[14] W. Hildenbrand Core and Equilibria of a Large Economy Princeton University Press, 1974.

[15] H. J. Keisler, Hyper nite model theory, in Logic Colloquium 76 (R. O. Gandy and J. M. E. Hyland, eds.) North-Holland, Amsterdam, 1977.

[16] M. A. Khan and N. Sagara, Weak sequential convergence in L1( ; X) and an exact version of Fatou's lemma, Journal of Mathematical Analysis and Applications 412 (2014), 554{563.

[17] M. A. Khan and Y. Zhang, Set-valued functions, Lebesgue extensions and saturated probability spaces, Advances in Mathematics 229 (2012), 1080{1103.

[18] P. A. Loeb, Conversion from nonstandard to standard measure spaces and applications in probability theory, Transactions of the American Mathematical Society 211 (1975), 113{122.

22 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue