Canonical Brownian Motion on the Diffeomorphism Group of the Circle

By S. Fang. 2002

61 citations recorded by the source corpus.

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Flows, coalescence and noise (2002, unknown): “The critical case was studied in [1, 12, 30].”
A study of a class of stochastic differential equations with non-Lipschitzian coefficients (2005, methodology): “Theorem E. Suppose that the coefficients σ and b satisfy the hypothesis (H 1) with ρ(s) = log s and the hypothesis (H 2) with r(s) = log 1/s . F or e> 0, consider the solution (X e )t≥0 of the stochastic differential equation dX e = √ eσ (X e )d Wt + b(X e )d t, X e = xo. (1.2)”
Stochastic and geometric analysis of two infinite-dimensional groups (2010, unknown): “Second, in contrast to Fang's method of interpreting Equation (1.1.1) " pointwise " as a family of stochastic differential equations on S 1 , I will interpret it as a sequence of stochastic differential equations on a sequence of " Hilbert " spaces.”