LEADER 01719nam 2200397 n 450 001 996394864403316 005 20221108044422.0 035 $a(CKB)3810000000009622 035 $a(EEBO)2248509498 035 $a(UnM)99829356 035 $a(UnM)9928078100971 035 $a(EXLCZ)993810000000009622 100 $a19950602d1699 uy | 101 0 $aeng 135 $aurbn||||a|bb| 200 04$aThe considerations of Drexelius upon death$b[electronic resource] $eFor well, sick, and dying persons. Done into English by a Fellow of the Royal Society 210 $aLondon $cprinted by S. Bridge, for H. Walwyn, at the Three Legs in the Poultrey, over against the Stocks Market$d1699 215 $a[20], 325 [i.e. 335], [1] p., [4] plates of leaves 300 $aDedication reads: To the right worshipful Sir James Houblon, Kt. Alderman of the City of London, and one of their representatives in Parliament. This translation of Drexelius is humbly dedicated by, sir, your worship's devoted servant. 300 $aRunning title: Considerations upon death. 300 $aIdentified on UMI microfilm (Early English books, 1641-1700) reel 2004 as Wing D2181A. 300 $aAn English translation of: De aeternitates considerationes. 300 $aWith a final advert. leaf. 300 $aReproduction of the original at the British Library. 330 $aeebo-0018 606 $aDeath$vEarly works to 1800 615 0$aDeath 700 $aDrexel$b Jeremias$f1581-1638.$0718089 801 0$bCu-RivES 801 1$bCu-RivES 801 2$bCStRLIN 801 2$bWaOLN 906 $aBOOK 912 $a996394864403316 996 $aThe considerations of Drexelius upon death$92318363 997 $aUNISA LEADER 07835nam 2201861 450 001 9910809577703321 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 $a9910809577703321 996 $aMarkov processes from K. Itô's perspective$9145814 997 $aUNINA