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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