Abstract
We study the properties of the noise (in the Tsirelson sense) that is generated by the solutions of the well-known Tanaka equation.
Similar content being viewed by others
REFERENCES
H. Tanaka and M. Hasegawa, “Stochastic differential equations,” Jpn. Sem. Probab., 17(1964).
A. V. Skorokhod, “Stochastic equations for diffusion processes in a bounded region,” Teor. Ver. Primen., 6, 264–274 (1961).
N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes, North-Holland & Kodansha, Amsterdam–Tokyo (1989).
B. Tsirelson, Within and beyond the Reach of Brownian Innovation, Preprint, ICM (1998).
B. Tsirelson, Unitary Brownian Motions are Linearizable, Preprint (1998).
B. Tsirelson, Scaling Limit of Fourier–Walsh Coefficients (a Frame Work), Preprint (1999).
J. Warren, Splitting: Tanaka's SDE Revisited, Preprint.
H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge (1990).
T. E. Harris, “Coalescing and noncoalescing stochastic flows in R 1,” Stochast. Process. Their Appl., 17, 187–210 (1984).
A. Yu. Veretennikov and N. V. Krylov, “On explicit formulas for solutions of stochastic equations,” Math. USSR Sb., 29, 239–256 (1976).
K. Itô and H. P. McKean, Jr., Diffusion Processes and Their Sample Paths, Springer, Berlin (1965).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Watanabe, S. Stochastic Flow and Noise Associated with the Tanaka Stochastic Differential Equation. Ukrainian Mathematical Journal 52, 1346–1365 (2000). https://doi.org/10.1023/A:1010319800544
Issue Date:
DOI: https://doi.org/10.1023/A:1010319800544