This monograph explores the theoretical foundations of causal analysis for stochastic systems evolving in continuous time. It develops a framework of causality concepts based on information structures and prediction, extending ideas originally formulated for discrete-time processes to a much broader continuous-time setting. Conditional independence and conditional orthogonality serve as unifying principles throughout the text, providing a common language for formulating causal relationships across different stochastic structures and for studying how information, prediction, and dependence interact in continuous-time models. Applications are discussed in areas where continuous-time models arise naturally, such as econometrics, finance, neuroscience, stochastic control, and statistics.

The book is intended for researchers and graduate students in probability, statistics, stochastic processes, and related mathematical sciences who are interested in the theoretical foundations and applications of causal analysis.

Ljiljana Petrović received a M.Sc. degree in mathematics at the Faculty of Mathematics in the University of Belgrade, Serbia in 1981 and she completed her PhD thesis in 1988 at the Faculty of Sciences in the University of Kragujevac, Serbia. She is a chair of the seminar Stochastic with Applications organized by the Mathematical Institute of the Serbian Academy of Sciences and Arts. Her research interests include stochastic processes, stochastic differential equations, stochastics dynamical systems, statistics, finance and insurance.