Renewal theorems and stability for the reflected process

DOI10.1016/j.spa.2008.06.009zbMath1163.60308OpenAlexW2154746747MaRDI QIDQ1016615

Ross A. Maller, Ronald Arthur Doney, Mladen Svetoslavov Savov

Publication date: 6 May 2009

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spa.2008.06.009

zbMATH Keywords

reflected processovershootrenewal theoremspassage times

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Central limit and other weak theorems (60F05) Sums of independent random variables; random walks (60G50) Strong limit theorems (60F15) Stopping times; optimal stopping problems; gambling theory (60G40) Renewal theory (60K05)

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Cites Work

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• Cramér's estimate for a reflected Lévy process
• The growth of random walks and Levy processes
• On the position of a random walk at the time of first exit from a sphere
• Which i.i.d. sums are recurrently dominated by their maximal terms?
• The Russian option: Reduced regret
• Gambler's ruin and the first exit position of random walk from large spheres
• Infinite limits and infinite limit points of random walks and trimmed sums
• Divergence of a random walk through deterministic and random subsequences
• Stability and other limit laws for exit times of random walks from a strip or a halfplane
• Stability of the overshoot for Lévy processes
• Characterization of large price variations in financial markets
• On conditioning a random walk to stay nonnegative
• \(L^ p\)-boundedness of the overshoot in multidimensional renewal theory
• Curve crossing for random walks reflected at their maximum
• The key renewal theorem for a transient Markov chain
• Heavy tails in multi-server queue
• The maximum of a random walk reflected at a general barrier
• Passage times of random walks and Lévy processes across power law boundaries
• Russian and American put options under exponential phase-type Lévy models.
• Estimates for Overshooting an Arbitrary Boundary by a Random Walk and Their Applications
• Random walks crossing curved boundaries: a functional limit theorem, stability and asymptotic distributions for exit times and positions
• Conditional limit theorems for asymptotically stable random walks
• On the rate of growth of the overshoot and the maximum partial sum
• On Compactness Properties of the Exit Position of a Random Walk From an Interval
• Conditional limit theorems for spectrally positive Lévy processes
• On the maximum drawdown of a Brownian motion