Svetlozar T. Rachev, Ludger Rüschendorf's Mass Transportation Problems: Applications PDF

By Svetlozar T. Rachev, Ludger Rüschendorf

ISBN-10: 038798352X

ISBN-13: 9780387983523

This can be the 1st entire account of the speculation of mass transportation difficulties and its functions. In quantity I, the authors systematically boost the speculation of mass transportation with emphasis to the Monge-Kantorovich mass transportation and the Kantorovich-Rubinstein mass transshipment difficulties, and their a variety of extensions. They speak about quite a few assorted ways in the direction of suggestions of those difficulties and take advantage of the wealthy interrelations to numerous mathematical sciences--from useful research to chance idea and mathematical economics. the second one quantity is dedicated to functions to the mass transportation and mass transshipment difficulties to issues in utilized likelihood, thought of moments and distributions with given marginals, queucing conception, possibility concept of likelihood metrics and its purposes to varied fields, amoung them basic restrict theorems for Gaussian and non-Gaussian proscribing legislation, stochastic differential equations, stochast! ic algorithms and rounding difficulties. The publication can be beneficial to graduate scholars and researchers within the fields of theoretical and utilized probabilitry, operations study, desktop technology, and mathematical economics. the must haves for this e-book are graduate point chance conception and actual and sensible research.

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Extra resources for Mass Transportation Problems: Applications

Example text

For simplicity, let us consider the 2-dimensional case. Let θ1 , . . , θn be n unit vectors in the plane and P1 , P2 be two probabilities on IR2 having the same marginals in the directions θ1 , . . , θn . To estimate the distance (1) Here weak metric stands for a metric metrizing the weak convergence in the space of probability measures on a Euclidean space.

M − 1, j = 1, . . , n − 1 . 27) if i = 0 or j = 0, where σrs = 0 if r = 0 or s = 0. f. with support on X × Y, X = (xi )i∈M , Y = (yj )j∈N . , i j dij := prs , i ∈ N, j ∈ M. 28) r=1 s=1 Proof: Consider the discrete version of F (cf. 25)). 29) 0 if i = 0 or j = 0. 22). If i = j = 1, then p11 = min(a1 , b1 , σ11 ) (cf. 29) d11 = min{σ11 + a1 + b1 , σ11 + a1 , σ10 + b1 , σ11 } = p11 . Suppose we have proved that d1,j−1 = p11 + · · · + p1,j−1 . 3 Mass Transportation Problems with Capacity Constraints j−1 j−1 p1s + min a1 − = s=1 = = 23 j−1 p1s , bj , σ1j − s=1 p1s s=1 min{a1 , bj + d1,j−1 , σ1,j } min{a1 , b1 + · · · + bj , σ11 + b2 + · · · + bj , .

17. 62) prs ≤ λij , i = 1, . . , m − 1, j = 1, . . , n − 1. n r=1 s=j Suppose i∈M ai = j∈N bj and c(·, ·) is a lattice superadditive sequence (cf. 51)). 63) hold. 61). Moreover, the optimal pij ’s are determined by pij = fij − fi,j+1 − fi−1,j + fi−1,j+1 , where fij := min {λrs + (ar+1 + · · · + ai ) + (bj + · · · + bs−1 )} 1≤r≤i j≤s≤n i n ar ∧ ∧ r=1 bs . 10). The results are motivated by Hoffman and Veinott (1990), where the discrete version of the problem has been considered. We shall only state the results.

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Mass Transportation Problems: Applications by Svetlozar T. Rachev, Ludger Rüschendorf

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