Stochastics

Since Jakob Bernoulli’s1 masterpiece Ars Conjectandi [1] was published in 1713, the science of stochastics or, better said, its methods have penetrated not only almost any field of scientific research but are also applied in an ever-increasing intensity in industry, administration, health care, and so forth. Nowadays, there is hardly any science which does not have a particular statistical branch. The reason for this development is very simple: Science investigates different real-world phenomena trying to understand and explain them. Stochastics deals with one of the most interesting and difficult aspect of any real-world phenomenon, namely the uncertainty with respect to its future development. Uncertainty itself is everywhere, and moreover, uncertainty is structured. Sometimes it is large, sometimes it is small, and often it is possible to manipulate it. Hence, uncertainty follows certain laws, which are different from situation to situation. Generally, it is not possible to completely remove uncertainty, even if its laws are known, but knowledge about the laws leads to a better control of uncertainty. In fact, a great part of any human activity aims at controlling the future development by controlling uncertainty.