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This collection honours Ron Doney's work and includes invited
articles by his collaborators and friends. After an introduction
reviewing Ron Doney's mathematical achievements and how they have
influenced the field, the contributed papers cover both
discrete-time processes, including random walks and variants
thereof, and continuous-time processes, including Le vy processes
and diffusions. A good number of the articles are focused on
classical fluctuation theory and its ramifications, the area for
which Ron Doney is best known.
This collection honours Ron Doney's work and includes invited
articles by his collaborators and friends. After an introduction
reviewing Ron Doney's mathematical achievements and how they have
influenced the field, the contributed papers cover both
discrete-time processes, including random walks and variants
thereof, and continuous-time processes, including Le vy processes
and diffusions. A good number of the articles are focused on
classical fluctuation theory and its ramifications, the area for
which Ron Doney is best known.
Derived from extensive teaching experience in Paris, this second
edition now includes over 100 exercises in probability. New
exercises have been added to reflect important areas of current
research in probability theory, including infinite divisibility of
stochastic processes, past-future martingales and fluctuation
theory. For each exercise the authors provide detailed solutions as
well as references for preliminary and further reading. There are
also many insightful notes to motivate the student and set the
exercises in context. Students will find these exercises extremely
useful for easing the transition between simple and complex
probabilistic frameworks. Indeed, many of the exercises here will
lead the student on to frontier research topics in probability.
Along the way, attention is drawn to a number of traps into which
students of probability often fall. This book is ideal for
independent study or as the companion to a course in advanced
probability theory.
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