小时间区间中的条件扩散过程

CONDITIONAL DIFFUSION PROCESSES IN A SMALL TIME IOTERVERVAL

  • 摘要: 本文讨论具有一致连续系数条件扩散过程的大偏差性质。设Xt)是具有Dirichlet空间(δ, H01Rd))的扩散过程,其中\varepsilon(f, g)=\frac12 \int_g^R\langle\nabla f, a \cdot \nabla g\rangle(x) d x。 Px,yσ是过程x6t)=xεt)满足条件x6(0)=x,x6(1)=y的律。那么当ε→0时,(Px,yσ)具有大偏差性质,且具有速率函数J_\sigma, y(\omega)=\frac12 \int_0^1\left\langle\dot\omega(t), a^-1(\omega(t)) \cdot \dot\omega(t)\right\rangle d t-\frac12 d^2(x, y)。

     

    Abstract: In this paper, we study the large deviation property of the conditional diffusion process-with uniformly continuous diffusion coefficents. Let Xt) be a diffusion process associated with the Dirichlet spaoe(δ, H01Rd))), where \varepsilon(f, g)=\frac12 \int_g^R\langle\nabla f, a \cdot \nabla g\rangle(x) d x and Px,yσ be the law of the process Xε(t)=Xεt) conditional onXε(0) = x and Xε(l)=y. Then wo show that (Xx,yσ) has large deviation property as ε→0 with the rate functionJ_\sigma, y(\omega)=\frac12 \int_0^1\left\langle\dot\omega(t), a^-1(\omega(t)) \cdot \dot\omega(t)\right\rangle d t-\frac12 d^2(x, y).

     

/

返回文章
返回