Weak limits of perturbed random walks and the equation \(Y_ t = B_ t+\alpha\sup\{Y_ s:s \leq t\} + \beta\inf\{Y_ s:s\leq t\}\)
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Publication:674516
DOI10.1214/aop/1041903215zbMath0870.60076OpenAlexW2010634466MaRDI QIDQ674516
Publication date: 30 July 1997
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1041903215
Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Brownian motion (60J65) Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics (82C41)
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Cites Work
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- Recurrence of reinforced random walk on a ladder
- Phase transition in reinforced random walk and RWRE on trees
- On skew Brownian motion
- Vertex-reinforced random walk
- An excursion approach to Ray-Knight theorems for perturbed Brownian motion
- Some extensions of the arc sine law as partial consequences of the scaling property of Brownian motion
- `True' self-avoiding walks with generalized bond repulsion on \(\mathbb{Z}\)
- The ``true self-avoiding walk with bond repulsion on \(\mathbb{Z}\): Limit theorems
- Generalized Ray-Knight theory and limit theorems for self-interacting random walks on \(\mathbb{Z}^ 1\)
- Enlacements du Mouvement Brownien Autour Des Courbes de L'Espace
- Beta Variables as Times Spent in [0, ∞[ By Certain Perturbed Brownian Motions
- Convergence of stochastic processes
- Reinforced random walk
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