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Additive Functions and Gaussian Measures

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Prokhorov and Contemporary Probability Theory

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 33))

Abstract

In this paper we examine infinite dimensional analogs of the measure theoretic variations of Cauchy’s classical functional equation for additive functions. In particular, we show that the a naïve generalization of the finite dimensional statement fails in infinite dimensions and show how it has to be altered to make it true. In the process, we develop various techniques which lead naturally to results about the structure of abstract Wiener spaces.

Mathematics Subject Classification (2010): 60G15, 60G60

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References

  1. de Bruijn, N.G.: On almost additive functions. Colloq. Math. 15, 59-63 (1966)

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  4. Stroock, D.: Probability Theory, An Analytic View, 2nd edn. Cambridge University Press, Cambridge (2011)

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  5. Stroock, D.: Maps that take Gaussian measures to Gaussian measures. Ill. J. Math. 54(4), 1343–1355 (2010)

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, McGill University, 805 Sherbrooke W. St., Montreal, Canada, H3C 0B9

    Linan Chen & Daniel W. Stroock

Authors
  1. Linan Chen
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  2. Daniel W. Stroock
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Corresponding author

Correspondence to Linan Chen .

Editor information

Editors and Affiliations

  1. Steklov Mathematical Institute, Russian Academy of Sciences, Gubkina Str. 8, Moscow, 119991, Russia

    Albert N. Shiryaev

  2. Courant Institute, New York University, Mercer Street 252, New York, 10012, New York, USA

    S. R. S. Varadhan

  3. Central Economics & Math. Institute, Russian Academy of Sciences, Nakhimovsky Pr. 47, Moscow, 117418, Russia

    Ernst L. Presman

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Chen, L., Stroock, D.W. (2013). Additive Functions and Gaussian Measures. In: Shiryaev, A., Varadhan, S., Presman, E. (eds) Prokhorov and Contemporary Probability Theory. Springer Proceedings in Mathematics & Statistics, vol 33. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33549-5_11

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