LEADER 03880nam0 22005773i 450 001 VAN00268531 005 20260826093359.542 017 70$2N$a9781461381907 035 40$a799197717 100 $a20231206d1982 |0itac50 ba 101 $aeng 102 $aUS 105 $a|||| ||||| 181 $ai$b e 182 $ab 183 $acr 200 1 $aMarkov Random Fields$fYu. A. Rozanov$gTransl. from the Russian by Constance M. Elson 210 $aNew York$cSpringer-Verlag$d1982 215 $aix, 201 p.$cill.$d24 cm 327 $aIn this book we study Markov random functions of several variables. What is traditionally meant by the Markov property for a random process (a random function of one time variable) is connected to the concept of the phase state of the process and refers to the independence of the behavior of the process in the future from its behavior in the past, given knowledge of its state at the present moment. Extension to a generalized random process immediately raises nontrivial questions about the definition of a suitable" phase state," so that given the state, future behavior does not depend on past behavior. Attempts to translate the Markov property to random functions of multi-dimensional "time," where the role of "past" and "future" are taken by arbitrary complementary regions in an appro­ priate multi-dimensional time domain have, until comparatively recently, been carried out only in the framework of isolated examples. How the Markov property should be formulated for generalized random functions of several variables is the principal question in this book. We think that it has been substantially answered by recent results establishing the Markov property for a whole collection of different classes of random functions. These results are interesting for their applications as well as for the theory. In establishing them, we found it useful to introduce a general probability model which we have called a random field. In this book we investigate random fields on continuous time domains. Contents CHAPTER 1 General Facts About Probability Distributions §1. 500 1$3VAN00268532$aMarkovskiye sluchaynyye polya$93643939 606 $a60G60$xRandom fields [MSC 2020]$3VANC023477$2MF 606 $a60H10$xStochastic ordinary differential equations [MSC 2020]$3VANC020682$2MF 606 $a60Jxx$xMarkov processes [MSC 2020]$3VANC019842$2MF 610 $aBrownian Motion$9KW:K 610 $aConditional Probability$9KW:K 610 $aFields$9KW:K 610 $aMarkov property$9KW:K 610 $aProbability distributions$9KW:K 610 $aProbability measures$9KW:K 610 $aProbability spaces$9KW:K 610 $aRandom fields$9KW:K 610 $aRandom functions$9KW:K 610 $aVector$9KW:K 620 $aUS$dNew York$3VANL000011 700 1$aRozanov$bYurii A.$3VANV082116$01427702 702 1$aElson$bConstance M.$3VANV220507$4730 712 $aSpringer $3VANV108073$4650 790 1$aRozanov, Yuri? Anatol?evich$zRozanov, Yurii A.$3VANV220338 790 1$aRozanov, Yu. A.$zRozanov, Yurii A.$3VANV260355 790 1$aRozanov, Y. A.$zRozanov, Yurii A.$3VANV260356 790 1$aRosanow, J. A.$zRozanov, Yurii A.$3VANV260357 790 1$aRosanov, Yu. A.$zRozanov, Yurii A.$3VANV260358 801 $aIT$bSOL$c20260918$gRICA 856 4 $uhttps://doi.org/10.1007/978-1-4613-8190-7$zE-book ? Accesso al full-text attraverso riconoscimento IP di Ateneo, proxy e/o Shibboleth 899 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$1IT-CE0120$2VAN08 912 $fN 912 $aVAN00268531 950 $aBIBLIOTECA DEL DIPARTIMENTO DI MATEMATICA E FISICA$d08DLOAD e-book 7576 $e08eMF7576 20231211 996 $aMarkovskiye sluchaynyye polya$93643939 997 $aUNICAMPANIA