Large Deviations of Random Vector Fields with Applications to Economics

Nummelin, Esa

doi:10.1006/aama.1999.0668

Cited by 4 publications

(5 citation statements)

References 26 publications

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“…Proof The mathematical result which leads to this theorem first appeared in Nummelin (2000a), Corollary 4.4, but its proof contains some errors. We provide a correct proof in this paper.…”

Section: Partial Observationmentioning

confidence: 97%

“…It is proved in Nummelin (2000a), Theorem 5, that the level set {I X ≤ δ} is also compact, so we have some b < ∞ such that…”

Section: Partial Observationmentioning

confidence: 98%

“…By utilizing the theory of large deviations, Nummelin proved the existence and convergence of the equilibrium prices in a general dependent case. The results in Nummelin (2000a) and Nummelin (2000b) do not depend on some special structures of the Y. Hou ( ) Department of Mathematics and Statistics, University of Helsinki, P.O. Box 68, FI-00014, Helsinki, Finland e-mail: yongming.hou@helsinki.fi agents such as independent and identically distributed (Bhattacharya and Majumdar 1973;Hildenbrand 1971), exchangeability and strong mixing (Bhattacharya and Majumdar 1973), lattice (Föllmer 1974) or dependency neighborhoods Rotar 2000 andRotar 2002).…”

Section: Introductionmentioning

confidence: 95%

“…For example, in Rotar (2000, 2002), Nummelin (2000aNummelin ( , 2000b, such probability law is required in calculating the expectation of the total excess demand function. Eventually the random equilibrium prices converge to some non-random prices in the convergence set which contains prices making such expectation of the total excess demand vanish.…”

Section: Introductionmentioning

confidence: 99%

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Some inference results on random pure exchange economies

Hou

2012

Ann Oper Res

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“…Proof The mathematical result which leads to this theorem first appeared in Nummelin (2000a), Corollary 4.4, but its proof contains some errors. We provide a correct proof in this paper.…”

Section: Partial Observationmentioning

confidence: 97%

“…It is proved in Nummelin (2000a), Theorem 5, that the level set {I X ≤ δ} is also compact, so we have some b < ∞ such that…”

Section: Partial Observationmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Some inference results on random pure exchange economies

Hou

2012

Ann Oper Res

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“…The using of the random field theory for economic research is an approach known in literature, e.g. : Arbia (1989;, Arbia & Prucha (2013), Arbia et al (2008;, Bronars & Jansen (1987), Case (1991), Case et al (1993), Christakos (2017), Conley (1999), Conley & Ligon (2002), Conley & Topa (2002), Dahl & Gonzalez-Rivera (2003a;2003b), de Luna & Genton (2004), Elhorst (2010;2012;2014), Guyon (1995), Ippoliti et al (2013), Jenish & Prucha (2009), Knopov (1999), Nummelin (2000), Quah (1993), Topa (2001), Vega & Elhorst (2014. Among Polish authors, for example, Przybycin (1992) and Zieliński (2002) should be mentioned, and the works by the author of the paper.…”

Section: Literature Reviewmentioning

confidence: 99%

Spatio-temporal modelling of economic phenomena in the context of reducing the dimensions of the random field

Szulc

2020

EiP

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Motivation: Clear spatial diversity and high variability in time of economic phenomena and the fact that they show dependencies in space and time dimensions, as well as the spatio-temporal dependencies, lead to the consideration of the phenomena in terms of random fields. On the other hand, applying methods and tools from the field of multidimensional stochastic processes called random fields is difficult due to the specificity of the economic data, in particular to a low number of the observations in space. Hence, there arises the problem of the reduction of the dimensions (especially the space dimension) of the random fields which define economic phenomena. Aim: The aim of the paper is to discuss a model that will reflect the structure of spatial connections and dependence in the spatio-temporal process, while reducing the dimension of space as a non-random argument of the random field. As a result, the set of N time series will be analysed. Therefore, we build a multiple-equation model of autoregressive character with a spatial structure of dependence. In the paper we discuss the advantages and cognitive values of such an approach to the study of economic phenomena in spatio-temporal terms. Results: The empirical example concerns the unemployment rate in Poland across provinces (NUTS2) in the period from January 2011 to April 2019. The data create spatio-temporal series which is the realisation of the two-dimensional random field. The model building strategy is based on a vector autoregressive (VAR) specification, where there are as many time series as the provinces. The study shows that the use of the concept of the conditional, with regard to space dimension, random field simplifies the economet

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On the existence and convergence of price equilibria for random economies

Nummelin¹

2000

Ann. Appl. Probab.

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Large Deviations of Random Vector Fields with Applications to Economics

Cited by 4 publications

References 26 publications

Some inference results on random pure exchange economies

Some inference results on random pure exchange economies

Spatio-temporal modelling of economic phenomena in the context of reducing the dimensions of the random field

On the existence and convergence of price equilibria for random economies

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