A martingale method for the convergence of a sequence of processes to a jump-diffusion process

DOI10.1007/BF01013317zbMath0417.60009OpenAlexW1991995257MaRDI QIDQ3207784

Harold J. Kushner

Publication date: 1980

Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01013317

zbMATH Keywords

weak convergencemartingale methodconvergence of a sequence of process to a jump- diffusion process

Mathematics Subject Classification ID

Martingales with continuous parameter (60G44) Convergence of probability measures (60B10)

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Fluctuations in certain dynamical systems with averaging ⋮ Weak convergence and approximations for partial differential equations with stochastic coefficients ⋮ Diffusion approximations for nonlinear phase locked loop-type systems with wide band inputs ⋮ A differential delay equation with wideband noise perturbations ⋮ Generalized threshold latent variable model ⋮ Approximating multiple itô integrals with "band limited" processes ⋮ Limits for parabolic partial differential equations with wide band stochastic coefficients andan application to filtering theory

Cites Work

• Semigroups of conditioned shifts and approximation of Markov processes
• Extensions of Trotter's operator semigroup approximation theorems
• Jump-Diffusion Approximations for Ordinary Differential Equations with Wide-Band Random Right Hand Sides
• Stability and Control of Stochastic Systems with Wide-band Noise Disturbances. I
• Asymptotic theory of mixing stochastic ordinary differential equations
• On Stochastic Processes Defined by Differential Equations with a Small Parameter
• Diffusion processes with continuous coefficients, I
• A General Theorem on the Convergence of Operator Semigroups
• Diffusion processes with boundary conditions
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