5 papers · 1 filter
Penalizations of Two-Dimensional Simple Random Walk by Direction-Dependent Excursion Counts and Edge-Crossing Counts
Syota Esaki, Kohki Iba
We study penalizations of the two-dimensional simple random walk by functions of direction-dependent excursion counts and edge-crossing counts. The former record completed excursio…
Fredholm and Sturm--Liouville Type Characterizations of the Limit Measure for the Kac Killing Penalization for Lévy Processes
Kohki Iba
We study the Kac killing penalization for a one-dimensional recurrent Lévy process. We prove that the limit process possesses two equivalent characterizations by a Fredholm equatio…
Elephant Random Walk Conditioned to Avoid Zero
Kohki Iba, Go Tokumitsu
We investigate the long-time limit of an elephant random walk conditioned to avoid zero and show that the resulting process admits a Skorokhod-type embedding into a three-dimension…
A Tanaka-Type Formula for Compact Sets and Equilibrium Measures of Lévy Processes
Kohki Iba, Victor Rivero
Tanaka's formula is a classical identity for Brownian motion, and Tsukada (2018) extended it to Lévy processes not necessarily symmetric. From a potential-theoretic point of view,…
Hitting Probabilities of Finite Points for One-Dimensional Lévy Processes
Kohki Iba
For a one-dimensional Lévy process, we derive an explicit formula for the probability of first hitting a specified point among a fixed finite set. Moreover, using this formula, we…