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This book consists of two strongly interweaved parts: the mathematical theory of stochastic processes and its applications to molecular theories of polymeric fluids. The comprehensive mathematical background provided in the first part should be equally useful in many other branches of engineering and the natural sciences. As a benefit from the second part one gains a more direct understanding of polymer dynamics, one can more easily identify exactly solvable models, and one can develop efficient computer simulation algorithms in a straightforward manner. In view of the examples and applications to problems from the front line of science, this volume may be used as a basic textbook or as a reference book. Program examples written in FORTRAN are available via ftp from ftp.springer.de/pub/chemistry/polysim/.