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As in the case of the two previous volumes published in 1986 and
1997, the purpose of this monograph is to focus the interplay
between real (functional) analysis and stochastic analysis show
their mutual benefits and advance the subjects. The presentation of
each article, given as a chapter, is in a research-expository style
covering the respective topics in depth. In fact, most of the
details are included so that each work is essentially self
contained and thus will be of use both for advanced graduate
students and other researchers interested in the areas considered.
Moreover, numerous new problems for future research are suggested
in each chapter. The presented articles contain a substantial
number of new results as well as unified and simplified accounts of
previously known ones. A large part of the material cov ered is on
stochastic differential equations on various structures, together
with some applications. Although Brownian motion plays a key role,
(semi-) martingale theory is important for a considerable extent.
Moreover, noncommutative analysis and probabil ity have a prominent
role in some chapters, with new ideas and results. A more detailed
outline of each of the articles appears in the introduction and
outline to assist readers in selecting and starting their work. All
chapters have been reviewed."
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