STOCHASTIC HEAT EQUATION ON ALGEBRA OF GENERALIZED FUNCTIONS

DOI10.1142/S0219025712500269zbMath1278.60106MaRDI QIDQ4923891

Hafedh Rguigui, Abdessatar Barhoumi, Habib Ouerdiane

Publication date: 27 May 2013

Published in: Infinite Dimensional Analysis, Quantum Probability and Related Topics (Search for Journal in Brave)

zbMATH Keywords

heat equationwhite noisePoisson equationextended-Gross Laplaciangeneralized stochastic calculus

Mathematics Subject Classification ID

White noise theory (60H40) Distributions on infinite-dimensional spaces (46F25)

Related Items (14)

Quantum white noise Feynman-Kac formula ⋮ Higher powers of analytical operators and associated ∗-Lie algebras ⋮ Euler's theorem for homogeneous white noise operators ⋮ Fractional number operator and associated fractional diffusion equations ⋮ The q-Gamma White Noise ⋮ Quantum white noise Gaussian kernel operators ⋮ Quantum fractional Ornstein-Uhlenbeck semigroups and associated potentials ⋮ Infinite degrees of freedom Weyl representation: Characterization and application ⋮ Characterization of the \texttt{QWN}-conservation operator and applications ⋮ Quantum \(\lambda\)-potentials associated to quantum Ornstein-Uhlenbeck semigroups ⋮ Quantum Ornstein-Uhlenbeck semigroups ⋮ Operator theory: quantum white noise approach ⋮ Generalized Riemann-Liouville and Liouville-Caputo time fractional evolution equations associated to the number operator ⋮ Generalized Bernoulli Wick differential equation

Cites Work

• Quantum Laplacian and applications
• Gross Laplacian acting on operators
• Semimartingales: A course on stochastic processes
• Lévy Laplacian of generalized functions on a nuclear space
• Potential theory associated with Uhlenbeck-Ornstein process
• White noise calculus and Fock space
• Probability representations of solutions to the heat equation
• A duality theorem between spaces of holomorphic functions of exponential growth
• EXOTIC LAPLACIANS AND ASSOCIATED STOCHASTIC PROCESSES
• CAUCHY PROBLEMS ASSOCIATED WITH THE LÉVY LAPLACIAN IN WHITE NOISE ANALYSIS
• UNITARITY OF KUO'S FOURIER–MEHLER TRANSFORM
• THE LÉVY LAPLACIAN ACTING ON POISSON NOISE FUNCTIONALS
• DIAGONALIZATION OF THE LÉVY LAPLACIAN AND RELATED STABLE PROCESSES
• ANALYTIC CHARACTERIZATION OF GENERALIZED FOCK SPACE OPERATORS AS TWO-VARIABLE ENTIRE FUNCTIONS WITH GROWTH CONDITION
• A SIMILARITY BETWEEN THE GROSS LAPLACIAN AND THE LÉVY LAPLACIAN
• A QUANTUM APPROACH TO LAPLACE OPERATORS

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