随机宇宙学模型中的伊藤与斯特拉托诺维奇
Itô versus Stratonovich in a stochastic cosmological model
摘要：
在这项工作中，我们研究了随机版本的弗里德曼加速方程。这个模型已经在宇宙学文献中提出，作为对哈勃参数实验量化中发现的不确定性的一种可能解释。它的噪音被默认为Stratonovich意义上的。在这里，我们证明，这种解释导致有限时间爆破的解决方案，即哈勃参数的正概率。相比之下，如果我们只是将噪声解释修改为伊藤的解释，那么解几乎肯定全局存在。此外，在此解释下，预期的渐近行为也被发现。
英文摘要：
In this work we study a stochastic version of the Friedmann acceleration equation. This model has been proposed in the cosmology literature as a possible explanation of the uncertainty found in the experimental quantification of the Hubble parameter. Its noise has been tacitly interpreted in the Stratonovich sense. Herein we prove that this interpretation leads to a positive probability of finite time blow-up of the solution, that is, of the Hubble parameter. In contrast, if we just modify the noise interpretation to that of Itô, then the solution globally exists almost surely. Moreover, the expected asymptotic behavior is found under this interpretation too.
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