The complex Brownian motion as a strong limit of processes constructed from a Poisson process

DOI10.1016/j.jmaa.2016.06.061zbMath1345.60022arXiv1509.07116OpenAlexW2950110998MaRDI QIDQ530353

Xavier Bardina, Giulia Binotto, Carles Rovira

Publication date: 29 July 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.07116

zbMATH Keywords

strong convergenceweak convergencePoisson processcomplex Brownian motion

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Strong limit theorems (60F15) Brownian motion (60J65) Functional limit theorems; invariance principles (60F17) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (6)

Strong approximations of Brownian sheet by uniform transport processes ⋮ An explicit solution to the Skorokhod embedding problem for double exponential increments ⋮ Weak convergence of the complex fractional Brownian motion ⋮ On the strong convergence of multiple ordinary integrals to multiple Stratonovich integrals ⋮ Asymptotic behavior of the weak approximation to a class of Gaussian processes ⋮ Rate of convergence of uniform transport processes to a Brownian sheet

Cites Work

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• The Stratonovich heat equation: a continuity result and weak approximations
• A strong convergence to the Rosenblatt process
• Weak convergence for the stochastic heat equation driven by Gaussian white noise
• Approximations of fractional Brownian motion
• A strong uniform approximation of fractional Brownian motion by means of transport processes
• Lectures on topics in stochastic differential equations
• Rate of convergence of transport processes with an application to stochastic differential equations
• A stochastic model related to the telegrapher's equation
• Strong approximation of diffusion processes by transport processes
• A \(d\)-dimensional Brownian motion as a weak limit from a one-dimensional Poisson process
• Weak approximation of a fractional SDE
• Approximations of Fractional Stochastic Differential Equations by Means of Transport Processes
• A Strong Approximation of Subfractional Brownian Motion by Means of Transport Processes
• Rate of convergence of uniform transport processes to brownian motion and application to stochastic integrals
• Weak approximation for a class of Gaussian processes
• Almost Sure Convergence of Uniform Transport Processes to Brownian Motion
• Approximations of a complex Brownian motion by processes constructed from a Lévy process

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