考虑${<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="g">克</trans>}}_{\mathit{<trans\; data-src="n">n个</trans>}}<trans\; data-src=")">)</trans>}_{\mathit{<trans\; data-src="n">n个</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="1">1</trans>}}$独立同分布随机矩阵序列与左随机游动${\mathit{<trans\; data-src="G">G公司</trans>}}_{\mathit{<trans\; data-src="n">n个</trans>}}<trans\; data-src=":">:</trans><trans\; data-src="=">=</trans>{\mathit{<trans\; data-src="g">克</trans>}}_{\mathit{<trans\; data-src="n">n个</trans>}}<trans\; data-src="\dots ">\dots </trans>{\mathit{<trans\; data-src="g">克</trans>}}_{\mathrm{<trans\; data-src="1">1</trans>}}$,$\mathit{<trans\; data-src="n">n个</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="1">1</trans>}$关于一般线性群$<trans\; data-src="GL">德国劳埃德船级社</trans><trans\; data-src="(">(</trans>\mathit{<trans\; data-src="d">d日</trans>}<trans\; data-src=",">,</trans>\mathbb{<trans\; data-src="R">对</trans>}<trans\; data-src=")">)</trans>$在适当的条件下，我们为系数建立了Bahadur–Rao–Petrov型大偏差展开式$<trans\; data-src="⟨">⟨</trans>\mathit{<trans\; data-src="f">（f）</trans>}<trans\; data-src=",">,</trans>{\mathit{<trans\; data-src="G">G公司</trans>}}_{\mathit{<trans\; data-src="n">n个</trans>}}\mathit{<trans\; data-src="v">v（v）</trans>}<trans\; data-src="⟩">⟩</trans>$产品的${\mathit{<trans\; data-src="G">G公司</trans>}}_{\mathit{<trans\; data-src="n">n个</trans>}}$，其中$\mathit{<trans\; data-src="v">v（v）</trans>}<trans\; data-src="\in ">\in </trans>{\mathbb{<trans\; data-src="R">对</trans>}}^{\mathit{<trans\; data-src="d">d日</trans>}}$和$\mathit{<trans\; data-src="f">（f）</trans>}<trans\; data-src="\in ">\in </trans>{<trans\; data-src="(">(</trans>{\mathbb{<trans\; data-src="R">对</trans>}}^{\mathit{<trans\; data-src="d">d日</trans>}}<trans\; data-src=")">)</trans>}^{<trans\; data-src="\ast ">\ast </trans>}$特别是，我们在大偏差原理中获得了一个显式的速率函数，从而大大改进了已知的大偏差界。证明了系数的大偏差局部极限定理和概率测度变化下的大偏差展开式。