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008 120814s2012 sz | s |||| 0|eng d
020 _a9783034803700
_9978-3-0348-0370-0
024 7 _a10.1007/978-3-0348-0370-0
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aOsękowski, Adam.
_eauthor.
245 1 0 _aSharp Martingale and Semimartingale Inequalities
_h[electronic resource] /
_cby Adam Osękowski.
264 1 _aBasel :
_bSpringer Basel :
_bImprint: Birkhäuser,
_c2012.
300 _aXI, 462 p. 7 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aMonografie Matematyczne ;
_v72
505 0 _aPreface.- 1. Introduction.- 2. Burkholder’s method.- 3. Martingale inequalities in discrete time.- 4. Sub- and supermartingale inequalities in discrete time.- 5. Inequalities in continuous time.- 6. Inequalities for orthogonal semimartingales.- 7. Maximal inequalities.- 8. Square function inequalities -- Appendix -- Bibliography.
520 _aThis monograph presents a unified approach to a certain class of semimartingale inequalities, which can be regarded as probabilistic extensions of classical estimates for conjugate harmonic functions on the unit disc. The approach, which has its roots in the seminal works of Burkholder in the 1980s, makes it possible to deduce a given inequality for semimartingales from the existence of a certain special function with some convex-type properties. Remarkably, an appropriate application of the method leads to the sharp version of the estimate under investigation, which is particularly important for applications. These include the theory of quasiregular mappings (with major implications for the geometric function theory); the boundedness of two-dimensional Hilbert transforms and a more general class of Fourier multipliers; the theory of rank-one convex and quasiconvex functions; and more. The book is divided into a number of distinct parts. In the introductory chapter we present the motivation for the results and relate them to some classical problems in harmonic analysis. The next part contains a general description of the method, which is applied in subsequent chapters to the study of sharp estimates for discrete-time martingales; discrete-time sub- and supermartingales; continuous time processes; and the square and maximal functions. Each chapter contains additional bibliographical notes included for reference purposes.
650 0 _aMathematics.
650 0 _aFunctional analysis.
650 0 _aPotential theory (Mathematics).
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aPotential Theory.
650 2 4 _aFunctional Analysis.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783034803694
830 0 _aMonografie Matematyczne ;
_v72
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-0348-0370-0
912 _aZDB-2-SMA
999 _c101734
_d101734