Probability limit theorems in infinite-dimensional spaces give conditions un- der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep- arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in ...
Read More
Probability limit theorems in infinite-dimensional spaces give conditions un- der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep- arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.
Read Less
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $168.69, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2012 by Birkhauser.
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $176.87, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2012 by Birkhauser.
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $36.60, Sold by Zubal Books rated 5.0 out of 5 stars, ships from Cleveland, OH, UNITED STATES, published 1992 by Birkhauser.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
512 pp., Hardcover, NEW! ! . -If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $48.50, good condition, Sold by HPB-Red rated 5.0 out of 5 stars, ships from Dallas, TX, UNITED STATES, published 1992 by Birkhäuser.
Choose your shipping method in Checkout. Costs may vary based on destination.
Seller's Description:
Good. Connecting readers with great books since 1972! Used textbooks may not include companion materials such as access codes, etc. May have some wear or writing/highlighting. We ship orders daily and Customer Service is our top priority!
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $65.64, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Santa Clarita, CA, UNITED STATES, published 1992 by Birkhäuser.
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $168.69, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 1992 by Birkhauser.
Add this copy of Probability in Banach Spaces, 8: Proceedings of the to cart. $176.87, new condition, Sold by Ria Christie Books rated 4.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 1992 by Birkhauser.
