In this seminar, I trace the trajectory that begins with Markov chains, introduced at the end of the 19th century, and leads to Kolmogorov’s differential equations and, from there, to a family of psychometric models capable of describing the evolution of complex latent states. Following a historical introduction that places Markov and Kolmogorov within the so-called Russian school of probability, highlighting its theoretical continuity and methodological impact, I will show how their key concepts (limited dependence processes, state transitions, and the formalization of probability measurement) paved the way for longitudinal analysis in psychology.
In the second part, I will present the modelling framework I have recently developed to describe affective dynamics in terms of absorbing states: discrete- and continuous-time Markov chains are integrated with Kolmogorov’s forward equations and implemented through Monte Carlo sampling, allowing estimation of stability, inertia, and absorption times for clinically relevant states. I will discuss how this architecture provides interpretable indicators for both basic research and real-time monitoring of immersive digital interventions.
I will conclude by outlining potential applications, from the use of virtual reality for controlled elicitation of affective trajectories to the personalization of behavioural interventions through continuous estimation of transition probabilities. I will demonstrate how a solid anchoring in the Russian tradition of probability makes it possible to overcome the divide between mathematical models and clinical practice, offering a robust bridge between theory and contemporary psychological intervention. In particular, I will illustrate how the presence of absorbing states enables the quantification of emotional chronicity risk, thereby supporting data-driven therapeutic decision-making.
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