Stochasticity in Processes

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This book has evolved over fifteen years from a modern course on stochastic chemical kinetics aimed at graduate students in physics, chemistry, and biology. The first part systematically compiles the mathematical foundations necessary for understanding probability, statistics, and stochastic processes, which are essential for tackling the complex applications in chemistry and life sciences explored in the second part. Recent advancements in techniques and the resolution of conventional experiments at nano-scales have been remarkable, enabling molecular spectroscopy to uncover insights into processes at scales where traditional theories struggle without a solid understanding of randomness and its origins. Current data accuracy allows for direct recording of fluctuations, making it crucial for observers to have a strong background in the mathematics of limited reproducibility to avoid interpretative artifacts. The content is organized modularly, permitting readers to skip more advanced sections if they focus on applications. Most derivations of analytical solutions for selected examples are provided in full to assist advanced readers in deriving their own solutions. The book maintains uniform notation throughout and includes a glossary to clarify key concepts discussed.