Convergence of \({\mathcal S}'\)-valued processes and space-time random fields

DOI10.1016/0022-1236(86)90078-9zbMath0589.46027OpenAlexW2084568013MaRDI QIDQ1074063

B. George

Publication date: 1986

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-1236(86)90078-9

zbMATH Keywords

Skorokhod spaceasymptotic analysis of particle systemsLévy continuity theoremnuclear space of distributionstight sequence of processes

Mathematics Subject Classification ID

Gaussian processes (60G15) Spaces defined by inductive or projective limits (LB, LF, etc.) (46A13) Functional limit theorems; invariance principles (60F17) Spaces determined by compactness or summability properties (nuclear spaces, Schwartz spaces, Montel spaces, etc.) (46A11) Topological linear spaces of test functions, distributions and ultradistributions (46F05)

Related Items (26)

Langevin equations for S'-valued Gaussian processes and fluctuation limits of infinite particle systems ⋮ An occupation time approach for convergence of measure-valued processes, and the death process of a branching system ⋮ A long range dependence stable process and an infinite variance branching system ⋮ Limit theorems for supercritical branching random fields with immigration ⋮ Non-Markovian fluctuation limits of infinite particle systems ⋮ Semimartingales on duals of nuclear spaces ⋮ Occupation time fluctuations of weakly degenerate branching systems ⋮ Markov properties of the fluctuation limit of a particle system ⋮ A functional ergodic theorem for the occupation time process of a branching system ⋮ Tightness and weak convergence of probabilities on the Skorokhod space on the dual of a nuclear space and applications ⋮ Occupation time limits of inhomogeneous Poisson systems of independent particles ⋮ Self-similar stable processes arising from high-density limits of occupation times of particle systems ⋮ Stability of a class of transformations of distribution-valued processes and stochastic evolution equations ⋮ A random field approach to weak convergence of processes ⋮ Particle picture approach to the self-intersection local time of density processes in \(\mathcal S^{\prime}(\mathbb R^d)\) ⋮ On microscopic derivation of a fractional stochastic Burgers equation ⋮ Occupation times of subcritical branching immigration systems with Markov motions ⋮ Generalized solutions of a class of nuclear-space-valued stochastic evolution equations ⋮ OCCUPATION TIME FLUCTUATION LIMITS OF INFINITE VARIANCE EQUILIBRIUM BRANCHING SYSTEMS ⋮ RIEMANN–LIOUVILLE PROCESSES ARISING FROM BRANCHING PARTICLE SYSTEMS ⋮ White noise in space and time and the cylindrical wiener process ⋮ White noise in space and time and the cylindrical wiener process ⋮ A CLASS OF FRACTIONAL BROWNIAN FIELDS FROM BRANCHING SYSTEMS AND THEIR REGULARITY PROPERTIES ⋮ Limit theorems for occupation time fluctuations of branching systems. I: long-range dependence ⋮ Limit theorems for occupation time fluctuations of branching systems. II: Critical and large dimensions ⋮ Distribution-valued heavy-traffic limits for the \(\mathrm{G}/\mathrm{GI}/\infty\) queue

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