On the windings of complex-valued Ornstein–Uhlenbeck processes driven by a Brownian motion and by a stable process

DOI10.1080/17442508.2014.1000904zbMath1408.60071arXiv1209.4027OpenAlexW2047001162MaRDI QIDQ2804009

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Publication date: 27 April 2016

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1209.4027

zbMATH Keywords

Lévy processessubordinationstochastic differential equationslimit theoremsstable processesplanar Brownian motionSpitzer's theoremexit time from a conecomplex-valued Ornstein-Uhlenbeck processbig and small windingsBougerol's identity in lawisotropic Markov processesOrnstein-Uhlenbeck processes driven by a stable processradial and angular processskew-product representationwindings

Mathematics Subject Classification ID

Processes with independent increments; Lévy processes (60G51) Central limit and other weak theorems (60F05) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Martingales with continuous parameter (60G44) Diffusion processes (60J60) Stochastic integrals (60H05) Stable stochastic processes (60G52)

Related Items

The winding of stationary Gaussian processes, Stable windings at the origin, Dynamics of Gamma Bursts in Local Field Potentials, Winding of a Brownian particle around a point vortex

Cites Work

• Unnamed Item
• Unnamed Item
• The Morris-Lecar neuron model embeds a leaky integrate-and-fire model
• The mean first rotation time of a planar polymer
• Sustained oscillations for density dependent Markov processes
• Windings of random walks
• Étude asymptotique de certains mouvements browniens complexes avec drift
• Asymptotic laws of planar Brownian motion
• A new proof of Spitzer's result on the winding of two dimensional Brownian motion
• Further asymptotic laws of planar Brownian motion
• Path dependent options on yields in the affine term structure model
• Windings of Brownian motion and random walks in the plane
• Bougerol's identity in law and extensions
• \(\alpha\) -self-similar Markov processes
• Integrability properties and limit theorems for the exit time from a cone of planar Brownian motion
• On a martingale associated to generalized Ornstein-Uhlenbeck processes and an application to finance
• Introductory lectures on fluctuations of Lévy processes with applications.
• Stable windings
• Recurrence times for the Ehrenfest model
• Non-Gaussian Ornstein–Uhlenbeck-based Models and Some of Their Uses in Financial Economics
• Windings of Planar Stable Processes
• The asymptotic joint distribution of windings of planar Brownian motion
• On D. Williams' “Pinching Method” and Some Applications
• Loi de l'indice du lacet Brownien, et distribution de Hartman-Watson
• Winding angle and maximum winding angle of the two-dimensional random walk
• Time Change Representation of Stochastic Integrals
• Asymptotic stability and spiraling properties for solutions of stochastic equations
• On Hitting Times of the Winding Processes of Planar Brownian Motion and of Ornstein--Uhlenbeck Processes via Bougerol's identity
• Semi-stable Markov processes. I
• Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process¹
• On the First Passage Time Probability Problem
• Ergodic Property of the Brownian Motion Process
• The accuracy of Cauchy approximation for the windings of planar Brownian motion