LEADER 03709nam 22007815 450 001 9910897979603321 005 20260121125437.0 010 $a9783031631900 010 $a3031631900 024 7 $a10.1007/978-3-031-63190-0 035 $a(CKB)36383529900041 035 $a(DE-He213)978-3-031-63190-0 035 $a(MiAaPQ)EBC31733027 035 $a(Au-PeEL)EBL31733027 035 $a(EXLCZ)9936383529900041 100 $a20241019d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aProbability Theory I $eRandom Variables and Distributions /$fby Andrea Pascucci 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (XXI, 382 p. 24 illus., 16 illus. in color.) 225 1 $aLa Matematica per il 3+2,$x2038-5757 ;$v165 311 08$a9783031631894 311 08$a3031631897 320 $aIncludes bibliographical references and index. 327 $a1 Measures and probability spaces -- 2 Random variables -- 3 Sequences of random variables -- 4 Conditional probability -- 5 Summary exercises -- Appendix A: Dynkin?s theorems -- Appencix B: Absolute continuity -- Appendix C: Uniform integrability. 330 $aThis book provides a concise yet rigorous introduction to probability theory. Among the possible approaches to the subject, the most modern approach based on measure theory has been chosen: although it requires a higher degree of mathematical abstraction and sophistication, it is essential to provide the foundations for the study of more advanced topics such as stochastic processes, stochastic differential calculus and statistical inference. The text originated from the teaching experience in probability and applied mathematics courses within the mathematics degree program at the University of Bologna; it is suitable for second- or third-year students in mathematics, physics, or other natural sciences, assuming multidimensional differential and integral calculus as a prerequisite. The four chapters cover the following topics: measures and probability spaces; random variables; sequences of random variables and limit theorems; and expectation and conditional distribution. The text includes a collection of solved exercises. 410 0$aLa Matematica per il 3+2,$x2038-5757 ;$v165 606 $aStochastic processes 606 $aMathematical physics 606 $aProbabilities 606 $aEconometrics 606 $aMathematics 606 $aStochastic Processes 606 $aTheoretical, Mathematical and Computational Physics 606 $aProbability Theory 606 $aQuantitative Economics 606 $aMathematics 606 $aProbabilitats$2thub 606 $aProcessos estocāstics$2thub 606 $aXarxes neuronals (Informātica)$2thub 608 $aLlibres electrōnics$2thub 615 0$aStochastic processes. 615 0$aMathematical physics. 615 0$aProbabilities. 615 0$aEconometrics. 615 0$aMathematics. 615 14$aStochastic Processes. 615 24$aTheoretical, Mathematical and Computational Physics. 615 24$aProbability Theory. 615 24$aQuantitative Economics. 615 24$aMathematics. 615 7$aProbabilitats 615 7$aProcessos estocāstics 615 7$aXarxes neuronals (Informātica) 676 $a519.2 700 $aPascucci$b Andrea$0475297 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910897979603321 996 $aProbability Theory I$94215128 997 $aUNINA