In this paper, we present a switching property for squared Bessel process. We prove that the starting point and the time parameter can be in a sense switched. As a consequence, we obtain new distributional dependencies among a squared Bessel process R, a Brownian motion with drift \( {B}^{\left(\mu \right)},\mu \ge 0,\left({B}_t^{\left(\mu \right)}:= {B}_t+\mu t\kern0.5em \mathrm{for}\ \mathrm{a}\ \mathrm{Brownian}\ \mathrm{motion}\ B\right), \) and an integral functional of geometric Brownian motion A(μ) connected by the Lamperti relation. Finally, we deduce a new explicit form of the joint distribution of the Lamperti triple \( \left({R}_T,{A}_t^{\left(\mu \right)},\exp \left(2{B}_t^{\left(\mu \right)}\right)\right) \) for fixed t > 0 andT > 0.

在本文中，我们提出了平方贝塞尔过程的开关性质。我们证明了起点和时间参数可以在某种意义上进行切换。结果，我们在平方贝塞尔过程R中获得了新的分布相关性，即具有漂移\（{B} ^ {\ left（\ mu \ right）}，\ mu \ ge 0，\ left（{B} _t ^ {\ left（\ mu \ right）}：= {B} _t + \ mu t \ kern0.5em \ mathrm {for} \ \ mathrm {a} \ \ mathrm {Brownian} \ \ mathrm {motion} \ B \ right），\）和通过Lamperti关系连接的几何布朗运动A（μ）的积分函数。最后，我们推导出Lamperti三元组\（\ left（{R} _T，{A} _t ^ {\ left（\ mu \ right）}，\ exp \ left（2 {B } _t ^ {\ left（\ mu \ right）} \ right）\ right）\）对于固定的t> 0和T> 0。