What is Stochastics?

What is Stochastics?

The word stochastics is a collective term for the areas of probability theory and statistics. This field of mathematics studies the mathematical modeling of random events and thus can be applied in virtually all empirical disciplines. Consider, for example, strategies for gambling, medicine (design and evaluation of clinical trials), climate research, quality control, weather predictions (rain probability of 70%), insurance (calculation of premiums), transport (study of queues - traffic light control), epidemiology (models for the spread of diseases), opinion surveys, banking (portfolio analysis, marketing strategies), telecommunications (modeling of distributions of duration of calls) or quantum physics.

In probability theory, random processes with fixed and specified known probabilities are investigated, while in statistics, conclusions about unknown probabilities should be drawn from observed data. Probability theory provides the mathematical basis for the theoretical investigation of statistical procedures.

The modern theory of probability has evolved since the mid-19th century, when Kolmogorov 1933 introduced a rigorous mathematical theory in this field. The first important contributions in statistics, which deal with data from population, trade and econometrics, can already be found in the 17th century [John Graunt, 1620 - 1674; William Pretty, 1623 - 1687]. Century [John Graunt, 1620 - 1674; William Pretty, 1623 - 1687]. Today, statistics and probability theory have developed to two distinct disciplines far beyond the boundary of mathematics. In statistics there are more than 500 specialized journals which are published periodically.