Explore a rigorous mathematical lecture on stochastic systems and their top Lyapunov exponents. Delve into the complex world of lower bounds as presented by Jacob Bedrossian in this 49-minute talk hosted by the International Mathematical Union. Gain insights into advanced concepts in stochastic analysis, dynamical systems, and probability theory. Examine the methodologies used to establish lower bounds on the top Lyapunov exponent and understand their significance in characterizing the long-term behavior of stochastic systems. Enhance your understanding of this crucial topic in applied mathematics and its implications for various fields, including physics, engineering, and financial modeling.