术语“基本更新定理”的详细信息

英译术语:

elementary renewal theorem

汉语语境:

更新计数过程的基本更新定理，更一般地，随机游动生成的计数过程的基本更新定理，是更新理论的重要组成部分。对于增量是独立同分布的情形，经典的更新理论已日趋成熟。但是在实践中，相关的增量往往不是相互独立的。那么，对于带某种相依增量的随机游动生成的计数过程，是否也可以建立相应的基本更新定理？在很长一段时间内，这一问题没有实质性的进展。

英语语境:

Update the counting process of basic update theorem, more generally, counting the generated random walk process basic update theorem, is an important part of the update theory. For incremental is independent identically distributed situation, the classical renewal theory has been increasingly mature. But in practice, the relevant incremental often is not independent of each other. Therefore, for bringing a dependent counts to generate incremental random walk process, whether can also set up a corresponding basic renewal theorem? For a long time, this problem has no substantial progress.