Abstract In this article, we focus upon a family of matrix valued stochastic processes and study the problem of determining the smallest time such that their Laplace transforms become infinite. In particular, we concentrate upon the class of Wishart processes, which have proved to be very useful in different applications by their ability in describing non-trivial dependence. Thanks to this remarkable property we are able to explain the behavior of the explosion times for the Laplace transforms of the Wishart process and its time integral in terms of the relative importance of the involved factors and their correlations.

中文翻译：

---

Wishart 过程的一些拉普拉斯变换的爆炸时间

摘要 在本文中，我们关注矩阵值随机过程族，并研究确定最小时间使得它们的拉普拉斯变换变为无穷大的问题。特别地，我们专注于 Wishart 过程的类别，这些过程已被证明在不同的应用中非常有用，因为它们能够描述非平凡的依赖关系。由于这一非凡的性质，我们能够根据所涉及因素的相对重要性及其相关性来解释 Wishart 过程的拉普拉斯变换的爆炸时间行为及其时间积分。