G. V. Ryabov, “Duality for coalescing stochastic flows on the real line”, Theory Stoch. Process., 2018, Volume 23(39), Issue 2,Pages <nobr>55

Duality for coalescing stochastic flows on the real line

G. V. Ryabov^ab

^a Institute of Mathematics, National Academy of Sciences of Ukraine, Department of the Theory of Stochastic Processes, 01024, Ukraine, Kiev-4, 3, Tereschenkivska st.
^b National Technical Unviersity of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Institute of Physics and Technology, Department of Information Security, 03056, Kyiv, Ukraine, 37, Peremohy ave.

Abstract: For a class of coalescing stochastic flows on the real line the existence of dual flows is proved. A stochastic flow and its dual are constructed as a forward and backward perfect cocycles over the same metric dynamical system. The metric dynamical system itself is defined on a new state space for coalescing flows. General results are applied to Arratia flows with drift.

Keywords: Stochastic flow, duality, random dynamical system, Arratia flow.

MSC: Primary 60K35, 37H05; 60J60

Language: English