Representations of the finite-dimensional point densities in Arratia flows with drift
Teoriâ slučajnyh processov, Tome 25 (2020) no. 1, pp. 25-36.

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We derive representations for finite-dimensional densities of the point process associated with an Arratia flow with drift in terms of conditional expectations of the stochastic exponentials appearing in the analog of the Girsanov theorem for the Arratia flow.
Keywords: Brownian web, Arratia flow, random measure, stochastic flow, Brownian bridge, point process.
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A. A. Dorogovtsev; M. B. Vovchanskii. Representations of the finite-dimensional point densities in Arratia flows with drift. Teoriâ slučajnyh processov, Tome 25 (2020) no. 1, pp. 25-36. http://geodesic.mathdoc.fr/item/THSP_2020_25_1_a1/

[1] A. A. Dorogovtsev, Meroznachnye protsessy i stokhasticheskie potoki [Measure-valued Processes and Stochastic Flows], Proceedings of Institute of Mathematics of NAS of Ukraine, Mathematics and its Applications, 66, Institute of Mathematics of NAS of Ukraine, Kiev, 2007 (Russian) | MR

[2] A. A. Dorogovtsev, “Krylov-Veretennikov expansion for coalescing stochastic flows”, Commun. Stoch. Anal., 6:3 (2012), 421–435 | MR

[3] A. A. Dorogovtsev, M. B. Vovchanskii, “On approximations of the point measures associated with the Brownian web by means of the fractional step method and the discretization of the initial interval”, Ukr. Math. J., 72:9 (2020), 1179–1194 | MR

[4] P. Gosselin, T. Wurzbacher, “An Itô type isometry for loops in $\mathbf {R}^d$ via the Brownian bridge”, Séminaire de probabilites de Strasbourg, 31 (1997), 225–231 | MR

[5] O. Kallenberg, Foundations of Modern Probability, Probability and its Applications, 2nd ed., Springer-Verlag, New York, 2002 | DOI | MR

[6] I. Karatzas, S. E. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed., Springer-Verlag, 1996 | MR

[7] V. Konarovskyi, V. Marx, Conditional Distribution of Independent Brownian Motions to Event of Coalescing Paths, 2020, arXiv: abs/2008.02568

[8] H.-H. Kuo, Gaussian measures in Banach spaces, Lecture Notes in Mathematics, 463, Springer-Verlag, Berlin, 1975 | DOI | MR

[9] R. Munasinghe, R. Rajesh, R. Tribe, O. Zaboronski, “Multi-scaling of the $n-$point density function for coalescing Brownian motions”, Communications in Mathematical Physics, 268 (2006), 717–725 | DOI | MR

[10] Ph. E. Protter, Stochastic integration and differential equations, Applications of Mathematics (New York), Stochastic Modelling and Applied Probability, 21, 2nd ed., Springer-Verlag, Berlin, 2004, 415 xiv+ p. pp. | MR

[11] R. Tribe, O. Zaboronski, “Pfaffian formulae for one dimensional coalescing and annihilating systems”, Electronic Journal of Probability, 16 (2011), 2080–2103 | DOI | MR

[12] V. Fomichov, “The distribution of the number of clusters in the Arratia flow”, Communications on Stochastic Analysis, 10:3 (2016), 257–270 | DOI | MR