Non-Local Differential Operators in Probability - Kirk Lecture

Explore the fascinating world of non-local differential operators in probability through this 59-minute Kirk Lecture delivered by Professor Luisa Beghin from the University of Rome La Sapienza. Delve into the active field of research surrounding nonlocal differential operators, with a focus on fractional-order operators and their applications. Discover the historical origins of fractional-order integrals and derivatives, dating back to the late 17th century, and learn about their modern applications across diverse fields such as biology, engineering, probability theory, physics, and image processing. Gain insights into the stochastic applications of non-local operators, particularly in the theory of anomalous diffusions and renewal processes. This lecture, presented at the Isaac Newton Institute for Mathematical Sciences as part of the Fractional Differential Equations programme, offers a comprehensive overview of this cutting-edge area of mathematical research.