LEADER 03151nam 22005655 450 001 9910734836003321 005 20260211152421.0 010 $a3-031-33772-7 024 7 $a10.1007/978-3-031-33772-7 035 $a(CKB)27451976500041 035 $a(MiAaPQ)EBC30618374 035 $a(Au-PeEL)EBL30618374 035 $a(DE-He213)978-3-031-33772-7 035 $a(PPN)272253278 035 $a(EXLCZ)9927451976500041 100 $a20230704d2023 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aNon-Gaussian Selfsimilar Stochastic Processes /$fby Ciprian Tudor 205 $a1st ed. 2023. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2023. 215 $a1 online resource (110 pages) 225 1 $aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4341 311 08$a9783031337710 327 $aIntroduction -- Chapter 1. Multiple Stochastic Integrals -- Chapter 2. Hermite processes: Definition and basic properties -- Chapter 3. The Wiener integral with respect to the Hermite process and the Hermite Ornstein-Uhlenbeck process -- Chapter 4. Hermite sheets and SPDEs -- Chapter 5. Statistical inference for stochastic (partial) differential equations with Hermite noise -- References. 330 $aThis book offers an introduction to the field of stochastic analysis of Hermite processes. These selfsimilar stochastic processes with stationary increments live in a Wiener chaos and include the fractional Brownian motion, the only Gaussian process in this class. Using the Wiener chaos theory and multiple stochastic integrals, the book covers the main properties of Hermite processes and their multiparameter counterparts, the Hermite sheets. It delves into the probability distribution of these stochastic processes and their sample paths, while also presenting the basics of stochastic integration theory with respect to Hermite processes and sheets. The book goes beyond theory and provides a thorough analysis of physical models driven by Hermite noise, including the Hermite Ornstein-Uhlenbeck process and the solution to the stochastic heat equation driven by such a random perturbation. Moreover, it explores up-to-date topics central to current researchin statistical inference for Hermite-driven models. 410 0$aSpringerBriefs in Probability and Mathematical Statistics,$x2365-4341 606 $aProbabilities 606 $aProbability Theory 606 $aApplied Probability 606 $aProcessos gaussians$2thub 606 $aIntegrals estocàstiques$2thub 608 $aLlibres electrònics$2thub 615 0$aProbabilities. 615 14$aProbability Theory. 615 24$aApplied Probability. 615 7$aProcessos gaussians 615 7$aIntegrals estocàstiques 676 $a519.2 700 $aTudor$b Ciprian$f1973-$01827123 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910734836003321 996 $aNon-Gaussian Selfsimilar Stochastic Processes$94395219 997 $aUNINA