On flows associated to Tanaka’s SDE and related works. (English) Zbl 1327.60118

Hajri, Hatem

Electron. Commun. Probab. 20, Paper No. 16, 12 p. (2015).

Summary: We review the construction of flows associated to Tanaka’s SDE. Using the skew Brownian motion, we give an easy proof of the classification of these flows by means of probability measures on \([0, 1]\). Our arguments also simplify some already available proofs.

MSC:

60H10	Stochastic ordinary differential equations (aspects of stochastic analysis)
60H25	Random operators and equations (aspects of stochastic analysis)
60J60	Diffusion processes
60J65	Brownian motion

Keywords:

stochastic flows; Tanaka’s stochastic differential equation; weak solutions; skew Brownian motion