Claude Dellacherie 
Capacités et processus stochastiques [PDF ebook] 

This book consists of two sections. The first section (A) is dealing with sets, capacities and measures of sets, giving elementary but deep theorems about approximation of measures and capacities for instance by compact sets. Besides concepts such as ‘paving capacity’ and ‘capacibility’ several modern and quite new concepts such as ‘capacitance’, ‘mosaic’, ‘envelope’, and ‘scarper’ (‘rabotage’) are introduces in order to describe refinements of the structure of classes of sets. Using these concepts the author proves in a new way know theorems such as Choquet”s theorem in abstract form and he also gives new theorems for instance theorems about analytic sets.

The second section (B) presents a general theory of stochastic processes but is mainly concerned with fundaments. It gives a far-reaching theory of stopping times and q-fields belonging to stopping times and classifications of stopping times and q-fields. This theory is then applied to stochastic processes, particularly to processes with realizations that are increasing functions. This book is well-fitted for researchers, who need a thorough knowledge of stochastic processes. H. Bergström.