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Autor:
J. Michael Steele
This lively, problem-oriented text, first published in 2004, is designed to coach readers toward mastery of the most fundamental mathematical inequalities. With the Cauchy-Schwarz inequality as the initial guide, the reader is led through a sequence
Autor:
Vladimir Pozdnyakov, J. Michael Steele
Publikováno v:
Mathematics Magazine. 89:167-176
The random—or orderly—seating of passengers on a bus is used to motivate several questions about cycles of permutations. These in turn motivates the investigation of bijections between special subs...
Autor:
Peichao Peng, J. Michael Steele
Publikováno v:
Proceedings of the American Mathematical Society. 144:4973-4982
We find a two term asymptotic expansion for the optimal expected value of a sequentially selected monotone subsequence from a random permutation of length n n . A striking feature of this expansion is that it tells us that the expected value of optim
Autor:
Petar Jevtic, J. Michael Steele
Publikováno v:
Mathematics of Operations Research. 40:992-1004
A caterpillar network (or graph) G is a tree with the property that removal of the leaf edges of G leaves one with a path. Here we focus on minimum weight spanning caterpillars where the vertices are points in the Euclidean plane and the costs of the
Publikováno v:
Operations Research. 62:864-875
We identify a rich class of finite-horizon Markov decision problems (MDPs) for which the variance of the optimal total reward can be bounded by a simple linear function of its expected value. The class is characterized by three natural properties: re
Autor:
Alessandro Arlotto, J. Michael Steele
Publikováno v:
Adv. in Appl. Probab. 46, no. 2 (2014), 536-559
We analyze the optimal policy for the sequential selection of an alternating subsequence from a sequence of $n$ independent observations from a continuous distribution $F$, and we prove a central limit theorem for the number of selections made by tha
Autor:
Vladimir Pozdnyakov, J. Michael Steele
Publikováno v:
Journal of Mathematical Analysis and Applications. 407:130-140
We illustrate a process that constructs martingales with help from matrix products that arise naturally in the theory of sampling without replacement. The usefulness of the new martingales is illustrated by the development of maximal inequalities for
Autor:
J. Michael Steele, Alessandro Arlotto
It is common in inventory theory to consider policies that minimize the expected cost of ordering and holding goods or materials. Nevertheless, the realized cost is a random variable, and, as the Saint Petersburg Paradox reminds us, the expected valu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f76215671e2f4ffd3d424d5f151ae300
http://arxiv.org/abs/1609.09141
http://arxiv.org/abs/1609.09141
Autor:
J. Michael Steele
Publikováno v:
Mathematica Applicanda. 44
The Bruss-Robertson inequality gives a bound on themaximal number of elements of a random sample whose sum is less than a specifiedvalue, and the extension of that inequality which is given hereneither requires the independence of the summands nor re
Autor:
Alessandro Arlotto, J. Michael Steele
Publikováno v:
Ann. Appl. Probab. 26, no. 4 (2016), 2141-2168
We construct a stationary ergodic process $X_1, X_2, \ldots $ such that each $X_t$ has the uniform distribution on the unit square and the length $L_n$ of the shortest path through the points $X_1, X_2, \ldots,X_n$ is not asymptotic to a constant tim