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Applications to Biology and Medicine

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An Introduction to Continuous-Time Stochastic Processes

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Abstract

This chapter is devoted to an analysis of fundamental results related to topics that have attracted the attention of a large number of scientists from many disciplines. The key issue is individual-based models and their approximation, leading to the so-called mean field models and to nonlinear PDEs. This category includes ant colonies, herd behavior, and swarm intelligence, all of which have generated a large and current body of research in biology, physics, operations research, economics, and related fields. An additional result refers to an important application of Itô-Lévy calculus to stochastic models in neurosciences.

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Authors and Affiliations

  1. ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences) and Department of Mathematics, University of Milan, Milan, Italy

    Vincenzo Capasso

  2. ADAMSS (Interdisciplinary Centre for Advanced Applied Mathematical and Statistical Sciences), University of Milan, Milan, Italy

    David Bakstein

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  1. Vincenzo Capasso
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  2. David Bakstein
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© 2012 Springer Science+Business Media New York

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Capasso, V., Bakstein, D. (2012). Applications to Biology and Medicine. In: An Introduction to Continuous-Time Stochastic Processes. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8346-7_6

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