Thesis supervisor: Gergely Mádi-Nagy
Location of studies (in Hungarian): Department of Operations Research, ELTE TTK Abbreviation of location of studies: ELTE
Description of the research topic:
"Recently a number of papers have been published about the univariate and multivariate discrete moment problem (DMP, MDMP), where bounding formulas as well as algorithmic bounds for functions of random variables under moment information are presented (see Prékopa 1990, 1998, Mádi-Nagy and Prékopa 2004, Mádi-Nagy 2009).Usually, the moments of order up to m of a random variable/vector are supposed to be known and lower and upper bounds for various functions of the random variable/vector have been proposed. These include bounds for probabilities of the type X >=a or X = a.
The objects are, on one hand, to develop effective solution algorithms for solving the MDMP. On the other hand, the application of MDMP in several fields, e.g., reliability theory, Boole-Bonferroni bounds etc.
G. MÁDI-NAGY, On Multivariate Discrete Moment Problems: Generalization of the Bivariate Min
Algorithm for Higher Dimensions, SIAM Journal on Optimization, 19, 4 (2009), 1781–1806.
G. MÁDI-NAGY, AND A. PRÉKOPA, On Multivariate Discrete Moment Problems and Their Applications to Bounding Expectations and Probabilities, Mathematics of Operations Research, 29, 2 (2004), 229–258.
A. PRÉKOPA, The Discrete Moment Problem and Linear Programming, Discrete Applied Mathematics, 27 (1990), 235–254.
A. PRÉKOPA, Bounds on Probabilities and Expectations Using Multivariate Moments of Discrete
Distributions, Studia Scientiarum Mathematicarum Hungarica, 34 (1998), 349–378."
Required language skills: english (working proficiency) Number of students who can be accepted: 1
Deadline for application: 2017-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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