scientific article; zbMATH DE number 408258

zbMath0771.60048MaRDI QIDQ4202615

Ludwig Streit, Hui-Hsiung Kuo, Takeyuki Hida, Juergen Potthoff

Publication date: 1 September 1993

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

zbMATH Keywords

white noise analysisDirichlet formsFeynman integralinfinite-dimensional Fourier transforminfinite- dimensional analogues of Laplaciansinfinite-dimensional Gaussian measuresprobabilistic structure of Brownian motion

Mathematics Subject Classification ID

Applications of stochastic analysis (to PDEs, etc.) (60H30) Generalized stochastic processes (60G20) Research exposition (monographs, survey articles) pertaining to probability theory (60-02)

Related Items

A white noise approach to infinitely divisible distributions on Gel'fand triple, Polynomials of Meixner's type in infinite dimensions: Jacobi fields and orthogonality measures, Measurements of ordinary and stochastic differential equations., Random fields as generalized white noise functionals, Construction of Malliavin differentiable strong solutions of SDEs under an integrability condition on the drift without the Yamada-Watanabe principle, Generalized fraction evolution equations with fractional Gross Laplacian, Chern--Simons theory on \(\mathbb R^3\) in axial gauge: a rigorous approach, Quantum mechanical propagators in terms of Hida distributions, Spaces of white noise distributions: Constructions, descriptions, applications. I, A fractional calculus interpretation of the fractional volatility model, Stochastic Volterra equations with singular kernels, Products and transforms of white-noise functionals (in general setting), Standardizing densities on Gaussian spaces, Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order, The stochastic linear quadratic optimal control problem in Hilbert spaces: a polynomial chaos approach, Variational theory and computations in stochastic plasticity, On a dual pair of spaces of smooth and generalized random variables, Infinite-dimensional non-Gaussian analysis and generalized translation operators, Dirichlet forms and white noise analysis, A note on the renormalized square of free quantum fields in space-time dimension \(d\geqslant 4\), Weighted stochastic Sobolev spaces and bilinear SPDEs driven by space-time white noise, A set-indexed fractional Brownian motion, Infinite dimensional oscillatory integrals with polynomial phase and applications to higher-order heat-type equations, A connection between the theory of hypergroups and white noise analysis, Path integrals on finite sets, A generalization of white noise analysis by means of theory of hypergroups, Wick calculus on spaces of generalized functions of compound Poisson white noise, A generalization of the Riesz representation theorem to infinite dimensions, Discrete-time multi-scale systems, Commutative Jacobi fields in Fock space, The Segal-Bargmann transform for Lévy functionals, Generalized parabolic functions on white noise space, A stochastic oscillator with time-dependent damping, A variational approach to the construction and Malliavin differentiability of strong solutions of SDEs, Law of large numbers and central limit theorem for Donsker's delta function of diffusions. I, An anticipatory Itô formula, Sampling-free linear Bayesian update of polynomial chaos representations, \(\gamma\)-product of white noise space and applications, Intersection local times of independent fractional Brownian motions as generalized white noise functionals, On the Tanaka formula for the derivative of self-intersection local time of fractional Brownian motion, Chaos decomposition and gap renormalization of Brownian self-intersection local times, Microstructures and rheology of micellar surfactant solution by Brownian dynamics simulation, Convergence theorems for generalized functional sequences of discrete-time normal martingales, Stochastic integral representation theorem for quantum semimartingales., Infinite dimensional oscillatory integrals as projective systems of functionals, Itô's lemma without non-anticipatory conditions, Infinite-dimensional stochastic differential equations obtained by subordination and related Dirichlet forms., A class of Gaussian processes with fractional spectral measures, A \(W\)-transform-based criterion for the existence of bounded extensions of \(E\)-operators., On the contraction property of energy forms on infinite-dimensional space, White noise analysis for Lévy processes., Inverse problem for the wave equation with a white noise source, Stochastic evolution equations with Wick-polynomial nonlinearities, Strong uniqueness for both Dirichlet operators and stochastic dynamics to Gibbs measures on a path space with exponential interactions, Quadratic actions, semi-classical approximation, and delta sequences in Gaussian analysis., A characterization of Hida distributions, Quaternion-valued positive definite functions on locally compact abelian groups and nuclear spaces, Characterization theorems for generalized functionals of discrete-time normal martingale, The Segal-Bargmann transform for Lévy white noise functionals associated with non-integrable Lévy processes, An infinite dimensional umbral calculus, Solutions of hyperbolic stochastic PDEs on bounded and unbounded domains, Local zeta functions, pseudodifferential operators and Sobolev-type spaces over non-Archimedean local fields, The Hamiltonian path integral for potentials of the Albeverio Høegh-Krohn class -- a white noise approach, Convergence theorems for operators sequences on functionals of discrete-time normal martingales, Algebraic and differential properties of polynomial Fourier transformation, Modelling non-Markovian fluctuations in intracellular biomolecular transport, Operator differential-algebraic equations with noise arising in fluid dynamics, Feynman path integrals for magnetic Schrödinger operators on infinite weighted graphs, A note on the invariance under change of measure for stochastic test functions and distribution spaces, Continuity of affine transformations of white noise test functionals and applications, Discrete Wick calculus and stochastic functional equations, Nonlinear stochastic differential equations containing generalized delta processes, On the generalized stochastic Dirichlet problem. I: The stochastic weak maximum principle, Explicit representation of strong solutions of SDEs driven by infinite-dimensional Lévy processes, Linear stochastic systems: a white noise approach, Construction of strong solutions of SDE's via Malliavin calculus, Quantum Laplacian and applications, Square integrable holomorphic functions on infinite-dimensional Heisenberg type groups, Chern-Simons models on \(S^2\times S^1\), torus gauge fixing, and link invariants. I, Integration by parts on the law of the reflecting Brownian motion, The Wilson loop observables of Chern-Simons theory on \({\mathbb{R}}^3\) in axial gauge, Quantum \(\lambda\)-potentials associated to quantum Ornstein-Uhlenbeck semigroups, Solving Wick-stochastic water waves using a Galerkin finite element method, Properties of delta functions of a class of observables on white noise functionals, A financial market with singular drift and no arbitrage, Laplace approximation of transition densities posed as Brownian expectations, Lévy Laplacians in Hida calculus and Malliavin calculus, A splitting/polynomial chaos expansion approach for stochastic evolution equations, Application of hierarchical matrices for computing the Karhunen-Loève expansion, Classical Dirichlet forms on topological vector spaces --- closability and a Cameron-Martin formula, Implementing symmetries of a free Bose field via white noise operators, Analysis of generalized Lévy white noise functionals, Gross Laplacian acting on operators, Multi-parameter transformation groups on white noise functionals, Meixner class of non-commutative generalized stochastic processes with freely independent values. I: A characterization, An approach via fractional analysis to non-linearity induced by coarse-graining in space, A complex scaling approach to sequential Feynman integrals, The Lévy Laplacian and stable processes, \(H\)-\(C^1\) maps and elliptic SPDEs with polynomial and exponential perturbations of Nelson's Euclidean free field, Rotation-invariant operators on white noise functionals, Analytic characterizations of infinite dimensional distributions, A Poisson algebra on the Hida test functions and a quantization using the Cuntz algebra, Stochastic differential equation for Brox diffusion, Chebyshev--Hermite Polynomials and Distributions of Polynomials in Gaussian Random Variables, Fermionic quantum orthogonalizations. I, Along Paths Inspired by Ludwig Streit: Stochastic Equations for Quantum Fields and Related Systems, Transition Probabilities for Processes with Memory on Topological Non-trivial Spaces, Generalized Scaling Operators in White Noise Analysis and Applications to Hamiltonian Path Integrals with Quadratic Action, Laplace Operators in Gamma Analysis, 38 Years with Professor Ludwig Streit, Generalized white noise analysis and topological algebras, The characterizations of Laplacians in white noise analysis, Non-Archimedean statistical field theory, Computational aspects of the stochastic finite element method, White noise approach to the construction of \(\Phi^{4}_{4}\) quantum fields. II, A Hida–Malliavin white noise calculus approach to optimal control, Significant edges in the case of non-stationary Gaussian noise, Towards non-perturbative quantization and the mass gap problem for the Yang–Mills field, Singular control of stochastic Volterra integral equations, An improved characterisation of regular generalised functions of white noise and an application to singular SPDEs, Grassmannian stochastic analysis and the stochastic quantization of Euclidean fermions, Non-Archimedean white noise, pseudodifferential stochastic equations, and massive Euclidean fields, $\delta $-function of an operator: A white noise approach, Spectral integrals of Bernoulli generalized functionals, Gaussian random fields: with and without covariances, White noise and simulation of ordinary Gaussian processes, On Lévy's Brownian motion and white noise space on the circle, Stochastic integrals and Gelfand integration in Fréchet spaces, Integral representation of generalized grey Brownian motion, Bessel SPDEs and renormalised local times, Stochastic quantization for the fractional Edwards measure, \(\gamma\)-quantum product of white noise operators and applications, Infinite-dimensional Lie algebras, representations, Hermitian duality and the operators of stochastic calculus, Analysis of stochastic quantization for the fractional Edwards measure, Construction of \(p\)-adic covariant quantum fields in the framework of white noise analysis, Flows for singular stochastic differential equations with unbounded drifts, A moment characterization of \(B\)-valued generalized functionals of white noise, The Stochastic LQR Optimal Control with Fractional Brownian Motion, On a class of quaternionic positive definite functions and their derivatives, Efficient White Noise Sampling and Coupling for Multilevel Monte Carlo with Nonnested Meshes, Solving SPDEs driven by colored noise: A chaos approach, Stochastic partial differential equations driven by multi-parameter white noise of Lévy processes, White noise differential equations for vector-valued white noise functionals, Hamiltonian path integrals in momentum space representation via white noise techniques, Stochastic finite elements: Computational approaches to stochastic partial differential equations, Solution to the stochastic Schrödinger equation on the full space, Inelastic Media under Uncertainty: Stochastic Models and Computational Approaches, An analytic characterization of \((p,q)\)-white noise functionals, Self-intersection local times for multifractional Brownian motion in higher dimensions: A white noise approach, White noise delta functions and infinite-dimensional Laplacians, Asymptotics of the evolution semigroup associated with a scalar field in the presence of a non-linear electromagnetic field, Fractional Langevin type equations for white noise distributions, The Taylor map on complex path groups, Stochastic integration via white noise analysis, Non-local Markovian symmetric forms on infinite dimensional spaces. I: The closability and quasi-regularity, ON WEIGHTEDL²(Ω)-SPACES, THEIR DUALS AND ITÔ INTEGRATION, Localization of quantum Bernoulli noises, Nonhomogeneous First-order Linear Malliavin Type Differential Equation, A white noise approach to the Feynman integrand for electrons in random media, On chirality and length-dependent potentials in polymer entanglements, On the paths Hölder continuity in models of Euclidean quantum field theory, Tail estimates for positive solutions of stochastic heat equation, Mittag-Leffler analysis. I: Construction and characterization, Optimal prediction for moment models: crescendo diffusion and reordered equations, Integral operators and dual orthogonal systems on a half-line^*, Notes on a 𝐶₀-group generated by the Lévy Laplacian, Global \(L_2\)-solutions of stochastic Navier-Stokes equations, Wiener chaos expansions and numerical solutions of randomly forced equations of fluid mechanics, Evolution equations with fractional Gross Laplacian and Caputo time fractional derivative, High order heat-type equations and random walks on the complex plane, Dynamical properties of endomorphisms, multiresolutions, similarity and orthogonality relations, Moment estimates for some renormalized parabolic Anderson models, A fractional PDE model for turbulent velocity fields near solid walls, Derivative of the Donsker delta functionals, Quantum integral equations of Volterra type in terms of discrete-time normal martingale, Schrödinger equation with Gaussian potential, Integration by parts on the law of the modulus of the Brownian bridge, Characterization of S-transform for general construction of infinite-dimensional distributions, Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis, Euclidean quantum field formulation of \(p\)-adic open string amplitudes, The elliptic stochastic quantization of some two dimensional Euclidean QFTs, A mathematical flat integral realization and a large deviation result for the free Euclidean field, Structure factors for generalized grey Browinian motion, A white noise approach to phase space Feynman path integrals, Stochastic equivariant cohomologies and cyclic cohomology, Imbedding of infinite dimensional distributions into simplified Colombeau type algebras, Discrete-time quantum Bernoulli noises, Pascal white noise harmonic analysis on configuration spaces and applications, Explicit formula for evolution semigroup for diffusion in Hilbert space, One dimensional parametrized test functions space of entire functions, Unnamed Item, Multilevel Quasi Monte Carlo Methods for Elliptic PDEs with Random Field Coefficients via Fast White Noise Sampling, Analytic characterization for Hilbert-Schmidt operators on Fock space, Solutions of infinite dimensional partial differential equations, Malliavin calculus for generalized and test stochastic processes, Binary jumps in continuum. I. Equilibrium processes and their scaling limits, Some cauchy problems in white noise analysis and associated semigroups of operators, White noise-based stochastic calculus with respect to multifractional Brownian motion, Stochastic analysis for a non-Markovian generator: an introduction, Wick calculus for vector-valued Gaussian white noise unctionals, Evolution systems and continuity equations for white noise functionals, Finite dimensional systems of free fermions and diffusion processes on spin groups, A white noise approach to stochastic currents of Brownian motion, Stochastic analysis for vector-valued generalized grey Brownian motion, Filtering theory for a weakly coloured noise process, On the local time of Gaussian and Lévy processes, Strong uniqueness for Dirichlet operators related to stochastic quantization under exponential/trigonometric interactions on the two-dimensional torus, Noncommutative quantum decomposition of Gegenbauer white noise process, Two generalizations of Mehler's formula in white noise analysis, Non-local Markovian symmetric forms on infinite dimensional spaces. II: Applications: non local stochastic quantization of space cut-off quantum fields and infinite particle systems, Generalized weighted number operators on functionals of discrete-time normal martingales, Mathematical Aspects of Feynman Path Integrals, Divergences, Quantum Fields and Diagrams, and Some More General Reflections, Elementary processes for Itô integral against cylindrical Wiener process, A biorthogonal approach to the infinite dimensional fractional Poisson measure, Form factors for stars generalized grey Brownian motion, Energy forms and quantum dynamics, Unnamed Item, Mathematical theory of Feynman path integrals, A fundamental solution to the Schrödinger equation with Doss potentials and its smoothness, On differential operators in white noise analysis, A Characterization of White Noise Test Functionals, A class of generalized Lévy Laplacians in infinite dimensional calculus, Stochastic calculus with respect to Gaussian processes, On the generalized stochastic Dirichlet problem. II: Solvability, stability and the Colombeau case, Modified diffusion with memory for cyclone track fluctuations, Mittag-Leffler analysis. II: Application to the fractional heat equation., Identification of Properties of Stochastic Elastoplastic Systems