This federal Project Grant award, provided by the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program, supports a collaborative research effort to systematically investigate stochastic functional systems. The $224,608 award, with a period of performance from August 1, 2024 to July 31, 2027, aims to (i) explore long-term properties of stochastic functional differential equations, (ii) formulate new approaches for McKean-Vlasov stochastic functional differential equations, and (iii) propose a framework for functional stochastic approximation algorithms. The research will apply these theoretical advancements to address real-world problems in areas such as ecology, infectious diseases, control engineering, neural networks, and data science. This multidisciplinary effort will also provide research opportunities for graduate students, engage high school students through math tournaments, and cultivate a network of academia, students, and industry to enhance career opportunities and public awareness of the role of mathematics in real-world applications.
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