This volume discusses the extended stochastic integral (ESI) (or Skorokhod-Hitsuda Integral) and its relation to the logarithmic derivative of differentiable measure along the vector or operator field. In addition, the theory of surface measures and the theory of heat potentials in infinite-dimensional spaces are discussed. These theories are closely related to ESI.It starts with an account of classic stochastic analysis in the Wiener spaces; and then discusses in detail the ESI for the Wiener measure including properties of this integral understood as a process. Moreover, the ESI with a nonrandom kernel is investigated.Some chapters are devoted to the definition and the investigation of properties of the ESI for Gaussian and differentiable measures.Surface measures in Banach spaces and heat potentials theory in Hilbert space are also discussed.Contents:Stochastic Calculus in Wiener SpaceExtended Stochastic Integral in Wiener SpaceRandomized Extended Stochastic Integrals with JumpsIntroduction to the Theory of Differentiable MeasuresExtended Vector Stochastic Integral in Sobolev Spaces of Wiener FunctionalsStochastic Integrals and Differentiable MeasuresDifferential Properties of Mixtures of Gaussian MeasuresSurface Measures in Banach SpaceHeat Potentials on Hilbert SpaceBibliographyIndexReadership: Mathematicians (Stochastic Analysis and Infinite-Dimensional Analysis).Key Features:Includes article coauthored by Samuel Kotz, Editor-in-Chief of Encyclopedia of Statistical SciencesProvides a tool for statisticians, economists, mathematicians and other researchers who are working on models theoryConsiders the most recent advances in models theory from methodological and practical points of view