This book provides an introductory albeit solid presentation of
path integration techniques as applied to the field of stochastic
processes. The subject began with the work of Wiener during the
1920's, corresponding to a sum over random trajectories,
anticipating by two decades Feynman's famous work on the path
integral representation of quantum mechanics. However, the true
trigger for the application of these techniques within
nonequilibrium statistical mechanics and stochastic processes was
the work of Onsager and Machlup in the early 1950's. The last
quarter of the 20th century has witnessed a growing interest in
this technique and its application in several branches of research,
even outside physics (for instance, in economy).The aim of this
book is to offer a brief but complete presentation of the path
integral approach to stochastic processes. It could be used as an
advanced textbook for graduate students and even ambitious
undergraduates in physics. It describes how to apply these
techniques for both Markov and non-Markov processes. The path
expansion (or semiclassical approximation) is discussed and adapted
to the stochastic context. Also, some examples of nonlinear
transformations and some applications are discussed, as well as
examples of rather unusual applications. An extensive bibliography
is included. The book is detailed enough to capture the interest of
the curious reader, and complete enough to provide a solid
background to explore the research literature and start exploiting
the learned material in real situations. remove
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