The limiting distribution of the mutual winding angles of particles in a Brownian stochastic flow with Lyapunov's zero top exponent

1Kuznetsov, VA
1Institute of Mathematics of the NAS of Ukraine, Kyiv
Dopov. Nac. akad. nauk Ukr. 2016, 9:14-22
Section: Mathematics
Language: Russian

The investigation of geometrical properties of particles moving in stochastic flows leads to the study of the limiting behaviour of their mutual winding angles. This problem is solved for isotropic Brownian stochastic flows with zero top Lyapunov exponent.

Keywords: Brownian stochastic flows, Lyapunov exponents, windings
  1. Yor M. Random Walks, Brownian Motion, and Interacting Particle Systems, Progress in Probability, Vol. 28, Boston: Birkhäuser, 1991: 441–455.
  2. Monin A.S., Yaglom I.M. Statistical Fluid Mechanics, Moscow: Nauka, 1967, Vol. 2 (in Russian).
  3. Le Jan Y. Z. Wahrscheinlichkeitstheor. verw. Gebiete, 1985, 70, No 1: 609–620.
  4. Kesten H., Papanicolaou G. Commun. Math. Phys., 1979, 65, No 2: 97–128.
  5. Kunita H. Stochastic Flows and Stochastic Differential Equations, Cambridge: Univ. Press, 1997.
  6. Zirbel C.L., Woyczyński W.A. Stoch. Dyn., 2002, 2, Iss. 1: 109–129.
  7. Yaglom A.M. Correlation Theory of Stationary and Related Random Functions, New York: Springer, 1987.
  8. Baxendale P.H. Lyapunov Exponents, Lecture Notes in Mathematics, Vol. 1186, New York: Springer, 1986: 322–337
  9. Zirbel C.L. Woyczyński W. Stoch. Proc. Appl., 1997, 69, No 2: 161–178.
  10. Thiffeault J.-L. Chaos, 2010, 20, Iss. 1: 017516.
  11. Kallenberg O. Foundations of Modern Probability, New York: Springer, 2002.
  12. Pitman J., Yor M. Ann. Probab., 1986, 14, No 3: 733–779.