Zhengdong Wang’s research while affiliated with Peking University and other places

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Publications (1)


Circulation of lifted processes on trivial principal bundles
  • Article

October 1997

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Science in China Series A Mathematics

Zhengdong Wang

A Brownian motion {x t }t⩾0 on a compact Riemannian manifold M with a drift vector field X can be lifted to a diffusion process{x~t}t0\left\{ {\tilde x_t } \right\}_{t \ge 0} on M × Tk corresponding to an ℝk valued smooth differential one-form A on M. The circulations (rotation numbers) of the lifted process{x~t}t0\left\{ {\tilde x_t } \right\}_{t \ge 0} around the k circles of Tk are studied. By choosing a certain ℝk -valued differential one-form A, these circulations give the hidden circulation of {x t }t⩾0 in M and the rotation numbers of {x t }t⩾0 around some closed curves in M which generalize the first homology group H1(M,ℤ) of M.