Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another

Bernt Oksendal; L. Csink

Annales de l'institut Fourier (1983)

  • Volume: 33, Issue: 2, page 219-240
  • ISSN: 0373-0956

Abstract

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We give several necessary and sufficient conditions that a function φ maps the paths of one diffusion into the paths of another. One of these conditions is that φ is a harmonic morphism between the associated harmonic spaces. Another condition constitutes an extension of a result of P. Lévy about conformal invariance of Brownian motion. The third condition implies that two diffusions with the same hitting distributions differ only by a chance of time scale. We also obtain a converse of the above theorem of Lévy.

How to cite

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Oksendal, Bernt, and Csink, L.. "Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another." Annales de l'institut Fourier 33.2 (1983): 219-240. <http://eudml.org/doc/74587>.

@article{Oksendal1983,
abstract = {We give several necessary and sufficient conditions that a function $\varphi $ maps the paths of one diffusion into the paths of another. One of these conditions is that $\varphi $ is a harmonic morphism between the associated harmonic spaces. Another condition constitutes an extension of a result of P. Lévy about conformal invariance of Brownian motion. The third condition implies that two diffusions with the same hitting distributions differ only by a chance of time scale. We also obtain a converse of the above theorem of Lévy.},
author = {Oksendal, Bernt, Csink, L.},
journal = {Annales de l'institut Fourier},
keywords = {harmonic spaces; conformal invariance of Brownian motion; hitting distributions},
language = {eng},
number = {2},
pages = {219-240},
publisher = {Association des Annales de l'Institut Fourier},
title = {Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another},
url = {http://eudml.org/doc/74587},
volume = {33},
year = {1983},
}

TY - JOUR
AU - Oksendal, Bernt
AU - Csink, L.
TI - Stochastic harmonic morphisms : functions mapping the paths of one diffusion into the paths of another
JO - Annales de l'institut Fourier
PY - 1983
PB - Association des Annales de l'Institut Fourier
VL - 33
IS - 2
SP - 219
EP - 240
AB - We give several necessary and sufficient conditions that a function $\varphi $ maps the paths of one diffusion into the paths of another. One of these conditions is that $\varphi $ is a harmonic morphism between the associated harmonic spaces. Another condition constitutes an extension of a result of P. Lévy about conformal invariance of Brownian motion. The third condition implies that two diffusions with the same hitting distributions differ only by a chance of time scale. We also obtain a converse of the above theorem of Lévy.
LA - eng
KW - harmonic spaces; conformal invariance of Brownian motion; hitting distributions
UR - http://eudml.org/doc/74587
ER -

References

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  14. [14] H. P. MCKEAN, Stochastic Integrals, Academic Press, 1969. Zbl0191.46603MR40 #947
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  16. [16] B. ØKSENDAL and D. W. STROOCK, A characterization of harmonic measure and Markov processes whose hitting distributions are preserved by rotations, translations and dilatations, Ann. Inst. Fourier, 32-4 (1982). Zbl0489.60078MR84g:60125
  17. [17] D. SIBONY, Allure à la frontière minimale d'une classe de transformations. Théorème de Doob généralisé, Ann. Inst. Fourier, 18 (1968), 91-120. Zbl0182.15002MR40 #395
  18. [18] D. W. STROOCK and S. R. S. VARADHAN, Multidimensional Diffusion Processes, Springer-Verlag, 1979. Zbl0426.60069MR81f:60108

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