journal6 ›› 2002, Vol. 23 ›› Issue (2): 59-61.

• Mathematics • Previous Articles     Next Articles

Stochastic Calculus on the Frame Bundle


  1. (First Teachers’ College of Hunan, Changsha 410002,China)
  • Online:2002-06-15 Published:2013-01-05

Abstract: Associated with a canonical second order differential operator on frame bandles, there is a diffusion process.We denote by X={x∈C([0,1],Rd),x(x)=0},H={h∈X:‖h‖2H=∫10|h··(t)|2dt<∞},Y={y∈C([0,1],s(d)):y(0)=0},K={k∈Y:‖k‖2K=∫10|k·(t)|2dt<∞},then (β,ρ) is a Rd×s(d)-valued semimartingale satisfying the following SDE:dβ(t)=dh(t)+ρdx(t)-(dy(t))β,β(0)=0,dρ(t)=dk(t)+Ω(dx(t),β(t))+[ρ(t),dy(t)],ρ(0)=0.

Key words: diffusion process, ItO map, differential calculus

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