Walsh's Brownian motion and Donsker scaling limits of perturbed random walks

DOI10.30757/alea.v21-63MaRDI QIDQ6634821

Ilya Pavlyukevich, Andrey Pilipenko

Publication date: 8 November 2024

Published in: ALEA. Latin American Journal of Probability and Mathematical Statistics (Search for Journal in Brave)

zbMATH Keywords

local timeperturbed random walkskew Brownian motionWalsh Brownian motionoscillating Brownian motionperturbed Markov chainDonsker scaling limitoscillating skew Brownian motion

Mathematics Subject Classification ID

Martingales with discrete parameter (60G42) Sums of independent random variables; random walks (60G50) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Markov chains (discrete-time Markov processes on discrete state spaces) (60J10) Processes in random environments (60K37) Functional limit theorems; invariance principles (60F17) Local time and additive functionals (60J55)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the limit behavior of a sequence of Markov processes perturbed in a neighborhood of the singular point
• On the constructions of the skew Brownian motion
• Periodic homogenization with an interface: the one-dimensional case
• On skew Brownian motion
• Convergence to diffusions with regular boundaries
• Limit theorems for random walks that avoid bounded sets, with applications to the largest gap problem
• On a skew stable Lévy process
• Functional limit theorems for random walks perturbed by positive alpha-stable jumps
• Stochastic-Process Limits
• Limit behavior of symmetric random walks with a membrane
• A functional limit theorem for locally perturbed random walks
• Limit theorem for perturbed random walks
• Stopped Random Walks
• A Topological Version of Slutsky's Theorem
• Oscillating Brownian motion
• Limit diffusion process for a non-homogeneous random walk on a one-dimensional lattice
• On a limit behaviour of a random walk penalised in the lower half-plane
• Markov chains on graphs and Brownian motion
• Boundary approximation for sticky jump-reflected processes on the half-line
• Limit behaviour of random walks on ℤ^mwith two-sided membrane

This page was built for publication: Walsh's Brownian motion and Donsker scaling limits of perturbed random walks