Bessel流的正则性
On regularity properties of Bessel flow
摘要：
研究了贝塞尔流$ρ: x \to ρ^x_t$的可微性，其中$(ρ^x_t)_{t\geq 0}$是从$x$出发的$δ>1$维BES（$^x(δ$）过程.对于$δ\geq 2$，我们证明了P-a. s中双连续导数的存在性.在$x\geq 0$上的意义，并研究了导数在$x=0$上的渐近行为.对于$1< δ<2$，我们证明了在$x\geq 0$上存在具有概率意义导数的Bessel流的一个修正.本文研究了$τ_0(x)$是$(ρ^x_t)_{t\geq 0}$的第一个零点时，$t=τ_0(x)$上导数的渐近行为.
英文摘要：
We study the differentiability of Bessel flow $ρ: x \to ρ^x_t$, where $(ρ^x_t)_{t\geq 0}$ is BES $^x(δ$) process of dimension $δ>1$ starting from $x$. For $δ\geq 2$ we prove the existence of bicontinuous derivatives in P-a.s. sense at $x\geq 0$ and we study the asymptotic behaviour of the derivatives at $x=0$. For $1< δ<2$ we prove the existence of a modification of Bessel flow having derivatives in probability sense at $x\geq 0$. We study the asymptotic behaviour of the derivatives at $t=τ_0(x)$ where $τ_0(x)$ is the first zero of $(ρ^x_t)_{t\geq 0}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
