Some applications of stochastic integration in infinite dimensions

DOI10.1080/17442508208833221zbMath0485.60056OpenAlexW1967029882MaRDI QIDQ3945323

Ali Süleyman Üstünel

Publication date: 1982

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442508208833221

zbMATH Keywords

semimartingalesOrnstein- Uhlenbeck processIto-Stratonovich formulastochastic integration on nuclear spaces

Mathematics Subject Classification ID

Random fields (60G60) Generalizations of martingales (60G48) Diffusion processes (60J60) Stochastic integrals (60H05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15)

Related Items

Langevin equations for S'-valued Gaussian processes and fluctuation limits of infinite particle systems ⋮ Applications of integration by parts formula for infinite-dimensional semimartingales ⋮ Stability of a class of transformations of distribution-valued processes and stochastic evolution equations ⋮ Hypoellipticity of the stochastic partial differential operators ⋮ THE MONOTONICITY INEQUALITY FOR LINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS ⋮ Stochastic integration with respect to cylindrical semimartingales ⋮ Solutions of SPDE's associated with a stochastic flow ⋮ Analytic semimartingales and their boundary values ⋮ An \(\infty\)-dimensional inhomogeneous Langevin's equation

Cites Work

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• Construction of branching diffusion processes and their optimal stochastic control
• Generalized Ornstein-Uhlenbeck processes and infinite particle branching Brownian motions
• A characterization of semimartingales on nuclear spaces
• Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density