这是因为(理论概率论。申请。 11（1966）390–406）慢动作${\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}$在时间尺度多维平均设置中

$$\frac{\mathit{<trans\; data-src="d">d日</trans>}{\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src=")">)</trans>}{\mathit{<trans\; data-src="d">d日</trans>}\mathit{<trans\; data-src="t">吨</trans>}}<trans\; data-src="=">=</trans>\frac{\mathrm{<trans\; data-src="1">1</trans>}}{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}\mathit{<trans\; data-src="B">B类</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\xi ">\xi </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src="/">/</trans>{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>\mathbf{<trans\; data-src="+">+</trans>}\mathit{<trans\; data-src="b">b条</trans>}<trans\; data-src="(">(</trans>{\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\xi ">\xi </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src="/">/</trans>{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}^{\mathrm{<trans\; data-src="2">2</trans>}}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src="\in ">\in </trans><trans\; data-src="[">[</trans>\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="T">T型</trans>}<trans\; data-src="]">]</trans>$$

弱收敛为$\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}<trans\; data-src="\to ">\to </trans>\mathrm{<trans\; data-src="0">0</trans>}$到提供的扩散过程$\mathit{<trans\; data-src="E">E类</trans>}\mathit{<trans\; data-src="B">B类</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="x">x个</trans>}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\xi ">\xi </trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="s">秒</trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans><trans\; data-src="\equiv ">\equiv </trans>\mathrm{<trans\; data-src="0">0</trans>}$哪里ξ是一个足够快的混合随机过程。在本文中，我们证明了${\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}$和扩散家族${\mathrm{<trans\; data-src="\Xi ">\Xi </trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}$可以在一个公共的足够丰富的概率空间上重新定义，以便$\mathit{<trans\; data-src="E">E类</trans>}{<trans\; data-src="sup">啜饮</trans>}_{\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="T">T型</trans>}}<trans\; data-src="|">|</trans>{\mathit{<trans\; data-src="X">X（X）</trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src=")">)</trans><trans\; data-src="-">-</trans>{\mathrm{<trans\; data-src="\Xi ">\Xi </trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="t">吨</trans>}<trans\; data-src=")">)</trans>{<trans\; data-src="|">|</trans>}^{\mathrm{<trans\; data-src="2">2</trans>}\mathit{<trans\; data-src="M">M（M）</trans>}}<trans\; data-src="\le ">\le </trans>\mathit{<trans\; data-src="C">C类</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=")">)</trans>{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}^{\mathit{<trans\; data-src="\delta ">\delta </trans>}}$对一些人来说$\mathit{<trans\; data-src="C">C类</trans>}<trans\; data-src="(">(</trans>\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src=")">)</trans><trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\delta ">\delta </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$以及所有$\mathit{<trans\; data-src="M">M（M）</trans>}<trans\; data-src="\ge ">\ge </trans>\mathrm{<trans\; data-src="1">1</trans>}$，$\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$，其中所有${\mathrm{<trans\; data-src="\Xi ">\Xi </trans>}}^{\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}}<trans\; data-src=",">，</trans>\mathit{<trans\; data-src="\epsilon ">\epsilon </trans>}<trans\; data-src=">">></trans>\mathrm{<trans\; data-src="0">0</trans>}$具有相同的扩散系数，但潜在的布朗运动可能随着ε对于相应的离散时间平均设置，我们也获得了类似的结果。作为一个应用，我们考虑了Dynkin的具有涉及扩散的路径相关收益的博弈，并通过这种离散时间近似获得了此类博弈值计算的误差估计，这比扩散本身的标准离散化提供了更有效的计算工具。