LEADER 07835nam 2201861 450 001 9910791958803321 005 20230617011549.0 010 $a0-691-11542-7 010 $a1-4008-3557-7 024 7 $a10.1515/9781400835577 035 $a(CKB)2560000000080609 035 $a(EBL)1769088 035 $a(SSID)ssj0000409556 035 $a(PQKBManifestationID)12172155 035 $a(PQKBTitleCode)TC0000409556 035 $a(PQKBWorkID)10347827 035 $a(PQKB)10774156 035 $a(MiAaPQ)EBC1769088 035 $a(DE-B1597)447600 035 $a(OCoLC)888749095 035 $a(OCoLC)979579163 035 $a(DE-B1597)9781400835577 035 $a(Au-PeEL)EBL1769088 035 $a(CaPaEBR)ebr10910141 035 $a(CaONFJC)MIL637574 035 $a(EXLCZ)992560000000080609 100 $a20140829h20032003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aMarkov processes from K. Ito?'s perspective /$fDaniel W. Stroock 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2003. 210 4$d©2003 215 $a1 online resource (289 p.) 225 1 $aAnnals of Mathematics Studies ;$vNumber 155 300 $aDescription based upon print version of record. 311 $a1-322-06323-0 311 $a0-691-11543-5 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tPreface -- $tChapter 1. Finite State Space, a Trial Run -- $tChapter 2. Moving to Euclidean Space, the Real Thing -- $tChapter 3. Itô's Approach in the Euclidean Setting -- $tChapter 4. Further Considerations -- $tChapter 5. Itô's Theory of Stochastic Integration -- $tChapter 6. Applications of Stochastic Integration to Brownian Motion -- $tChapter 7. The Kunita-Watanabe Extension -- $tChapter 8. Stratonovich's Theory -- $tNotation -- $tReferences -- $tIndex 330 $aKiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes. 410 0$aAnnals of mathematics studies ;$vNumber 155. 606 $aMarkov processes 606 $aStochastic difference equations 610 $aAbelian group. 610 $aAddition. 610 $aAnalytic function. 610 $aApproximation. 610 $aBernhard Riemann. 610 $aBounded variation. 610 $aBrownian motion. 610 $aCentral limit theorem. 610 $aChange of variables. 610 $aCoefficient. 610 $aComplete metric space. 610 $aCompound Poisson process. 610 $aContinuous function (set theory). 610 $aContinuous function. 610 $aConvergence of measures. 610 $aConvex function. 610 $aCoordinate system. 610 $aCorollary. 610 $aDavid Hilbert. 610 $aDecomposition theorem. 610 $aDegeneracy (mathematics). 610 $aDerivative. 610 $aDiffeomorphism. 610 $aDifferentiable function. 610 $aDifferentiable manifold. 610 $aDifferential equation. 610 $aDifferential geometry. 610 $aDimension. 610 $aDirectional derivative. 610 $aDoob?Meyer decomposition theorem. 610 $aDuality principle. 610 $aElliptic operator. 610 $aEquation. 610 $aEuclidean space. 610 $aExistential quantification. 610 $aFourier transform. 610 $aFunction space. 610 $aFunctional analysis. 610 $aFundamental solution. 610 $aFundamental theorem of calculus. 610 $aHomeomorphism. 610 $aHölder's inequality. 610 $aInitial condition. 610 $aIntegral curve. 610 $aIntegral equation. 610 $aIntegration by parts. 610 $aInvariant measure. 610 $aItô calculus. 610 $aItô's lemma. 610 $aJoint probability distribution. 610 $aLebesgue measure. 610 $aLinear interpolation. 610 $aLipschitz continuity. 610 $aLocal martingale. 610 $aLogarithm. 610 $aMarkov chain. 610 $aMarkov process. 610 $aMarkov property. 610 $aMartingale (probability theory). 610 $aNormal distribution. 610 $aOrdinary differential equation. 610 $aOrnstein?Uhlenbeck process. 610 $aPolynomial. 610 $aPrincipal part. 610 $aProbability measure. 610 $aProbability space. 610 $aProbability theory. 610 $aPseudo-differential operator. 610 $aRadon?Nikodym theorem. 610 $aRepresentation theorem. 610 $aRiemann integral. 610 $aRiemann sum. 610 $aRiemann?Stieltjes integral. 610 $aScientific notation. 610 $aSemimartingale. 610 $aSign (mathematics). 610 $aSpecial case. 610 $aSpectral sequence. 610 $aSpectral theory. 610 $aState space. 610 $aState-space representation. 610 $aStep function. 610 $aStochastic calculus. 610 $aStochastic. 610 $aStratonovich integral. 610 $aSubmanifold. 610 $aSupport (mathematics). 610 $aTangent space. 610 $aTangent vector. 610 $aTaylor's theorem. 610 $aTheorem. 610 $aTheory. 610 $aTopological space. 610 $aTopology. 610 $aTranslational symmetry. 610 $aUniform convergence. 610 $aVariable (mathematics). 610 $aVector field. 610 $aWeak convergence (Hilbert space). 610 $aWeak topology. 615 0$aMarkov processes. 615 0$aStochastic difference equations. 676 $a519.2/33 686 $aSI 830$2rvk 700 $aStroock$b Daniel W.$042628 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910791958803321 996 $aMarkov processes from K. Itô's perspective$9145814 997 $aUNINA LEADER 05590nam 22006255 450 001 9910559396703321 005 20250411004733.0 010 $a3-030-84144-8 024 7 $a10.1007/978-3-030-84144-7 035 $a(MiAaPQ)EBC6951390 035 $a(Au-PeEL)EBL6951390 035 $a(CKB)21502463400041 035 $a(PPN)262168111 035 $a(DE-He213)978-3-030-84144-7 035 $a(EXLCZ)9921502463400041 100 $a20220411d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aInformation and Communication Technologies for Agriculture?Theme I: Sensors /$fedited by Dionysis D. Bochtis, Maria Lampridi, George P. Petropoulos, Yiannis Ampatzidis, Panos Pardalos 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (331 pages) 225 1 $aSpringer Optimization and Its Applications,$x1931-6836 ;$v182 311 08$a3-030-84143-X 320 $aIncludes bibliographical references. 327 $aSection I: Overview: Emerging Sensing Technologies for Precision Agriculture (Pardalos) -- Soil reflectance spectroscopy for supporting Sustainable Development Goals (Angelopoulou) -- Proximal sensing sensors for monitoring crop growth (Hallik) -- Section II: Wireless network systems applications: Experimental performance evaluation techniques of LoRa radio modules and exploitation for agricultural use (Loukatos) -- Evaluating the performance of a simulated softwarized agricultural wireless sensor network (M. Mostaco) -- Smart agriculture: A low-cost wireless sensor network approach (Angelis) -- Section III: Remote sensing applications: Potential of Sentinel-2 satellite and novel proximal sensor data fusion for agricultural applications (Pand?i?) -- Trends in satellite sensors and image time series processing methods for crop phenology monitoring (Verrelst) -- Drone imagery in support of orchards trees vegetation assessment based on spectral indices and deep learning (?andric) -- Section IV: Proximal sensing applications: What does the NDVI really tell us about crops? Insight from proximal spectral field sensors (Atherton) -- Geophysical sensors for mapping soil layers - a comparative case study using different electrical and electromagnetic sensors (Luck) -- Geoinformation technologies in pest management: mapping olive fruit fly population in olive trees (Papafilippaki) -- In-field experiments for performance evaluation of a new low-cost active multispectral crop sensor (Tagarakis). 330 $aThis volume is the first (I) of four under the main themes of Digitizing Agriculture and Information and Communication Technologies (ICT). The four volumes cover rapidly developing processes including Sensors (I), Data (II), Decision (III), and Actions (IV). Volumes are related to ?digital transformation? within agricultural production and provision systems, and in the context of Smart Farming Technology and Knowledge-based Agriculture. Content spans broadly from data mining and visualization to big data analytics and decision making, alongside with the sustainability aspects stemming from the digital transformation of farming. The four volumes comprise the outcome of the 12th EFITA Congress, also incorporating chapters that originated from select presentations of the Congress. The focus in this volume is on different aspects of sensors implementation in agricultural production (e.g., types of sensors, parameters monitoring, network types, connectivity, accuracy, reliability, durability, and needs to be covered) and provides variety of information and knowledge in the subject of sensors design, development, and deployment for monitoring agricultural production parameters. The book consists of four (4) Sections. The first section presents an overview on the state-off-the art in sensing technologies applied in agricultural production while the rest of the sections are dedicated to remote sensing, proximal sensing, and wireless sensor networks applications. Topics include: Emerging sensing technologies Soil reflectance spectroscopy LoRa technologies applications in agriculture Wireless sensor networks deployment and applications Combined remote and proximal sensing solutions Crop phenology monitoring Sensors for geophysical properties Combined sensing technologies with geoinformation systems . 410 0$aSpringer Optimization and Its Applications,$x1931-6836 ;$v182 606 $aOperations research 606 $aManagement science 606 $aInformation storage and retrieval systems 606 $aEnvironmental sciences$xMathematics 606 $aOperations Research, Management Science 606 $aInformation Storage and Retrieval 606 $aMathematical Applications in Environmental Science 615 0$aOperations research. 615 0$aManagement science. 615 0$aInformation storage and retrieval systems. 615 0$aEnvironmental sciences$xMathematics. 615 14$aOperations Research, Management Science. 615 24$aInformation Storage and Retrieval. 615 24$aMathematical Applications in Environmental Science. 676 $a630.2085 676 $a630.2085 702 $aBochtis$b Dionysis 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910559396703321 996 $aInformation and Communication Technologies for Agriculture?Theme I: Sensors$94375146 997 $aUNINA