![]() This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. ![]() We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. ![]() We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. Based on these lines, a stochastic framework is discussed that can deal with natural extremes under perpetual change, avoiding naïve methodologies which currently prevail. On the other hand, observations on long time series, most prominently by Hurst in Egypt, provided the empirical basis to understand change and its consequences in typical engineering tasks. The scientific background to study perpetual change has been developed by the Moscow School of Mathematics and most prominently Kolmogorov, who, among other achievements, laid the axiomatic foundation of probability theory and introduced the concept of stochastic processes. These have provided concrete evidence that climate has been perpetually changing. The omnipresence of change is confirmed by modernday geological and paleoclimatic studies. However change has been well known and well studied on philosophical and scientific grounds since the era of Heraclitus and Aristotle. The derivation and details of the algorithm are described in this paper, while in a companion paper we illustrate and showcase the proposed framework with a number of case studies, some of which are controlled synthetic examples and others real-world ones arising from interesting scientific problems.Ĭurrent-day scholars have rediscovered change and given particular emphasis on climate change. Theoretical considerations allow the development of an effective algorithm, applicable to large-scale open systems, which are neither controllable nor repeatable. Starting from the idea of stochastic causal systems, we extend it to the more general concept of hen-or-egg causality, which includes as special cases the classic causal, and the potentially causal and anti-causal systems. Our proposed approach is based on stochastics, in which events are replaced by processes. ![]() We thus choose to determine necessary conditions that are operationally useful in identifying or falsifying causality claims. However, reviewing various approaches to it over the entire knowledge tree, from philosophy to science and to scientific and technological applications, we locate several problems, which prevent these approaches from defining sufficient conditions for the existence of causal links. Causality is a central concept in science, in philosophy and in life. ![]()
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