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

Annales de l'institut Fourier (1983)

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

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topOksendal, 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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- [15] P. A. MEYER, Géométrie stochastique sans larmes. Sem. de Probabilités XV, Springer Lecture Notes in Math., 850, Springer-Verlag, 1981. Zbl0459.60046
- [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] 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
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