Abstract.
This paper gives a construction of sticky flows on the circle. Sticky flows give examples of stochastic flows of kernels that interpolates between Arratia’s coalescing flow and the deterministic diffusion flow. They are associated with systems of sticky independent Brownian particles on the circle, for some fixed parameter of stickyness. It is proved that the noise generated by Brownian sticky flows is black. A new proof of the fact that the noise of Arratia’s coalescing flow is black is given.
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References
Bertoin, J.: Lévy processes. Cambridge university press, 1996
Bouleau, N., Hirsch, F.: Dirichlet forms and analysis on Wiener spaces. De Gruyter, Berlin, 1991
Fukushima, M., Oshima, Y., Takeda, M.: Dirichlet forms and symmetric Markov processes. De Gruyter, Berlin, 1994
Le Jan, Y., Raimond, O.: Flows, coalescence and noise. math.PR/0203221, To appear in The Annals of Probability
Le Jan, Y., Raimond, O.: Sticky flows on the circle. arXiv:math.PR/0211387, 2002
Le Jan, Y., Raimond, O.: The noise of a Brownian sticky flow is black. arXiv:math.PR/0212269, 2002
Pitman, J.: Combinatorial Stochastic Processes. Saint Flour lecture notes, Juillet, 2002
Tsirelson, B.: Unitary Brownian motions are linearizable. math.PR/9806112, 1998
Tsirelson, B.: Scaling limit, noise, stability. Saint Flour lecture notes, Juillet, 2002
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Jan, Y., Raimond, O. Sticky flows on the circle and their noises. Probab. Theory Relat. Fields 129, 63–82 (2004). https://doi.org/10.1007/s00440-003-0324-9
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DOI: https://doi.org/10.1007/s00440-003-0324-9