9 papers
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…
Multi-point local time penalizations with various clocks for one-dimensional Lévy processes
Kohki Iba
We study the penalization problem with various clocks where the weight is given as the exponential functional of multi-point local times for one-dimensional Lévy processes. The lim…
Conditioning to avoid bounded sets for a one-dimensional Lévy processes
Kohki Iba
For several classes of bounded sets , the limit of a one-dimensional Lévy process conditioned to avoid up to a parametrized random time which tends to infinity. For we t…
Conditionings to avoid points with various clocks for Lévy processes
Kohki Iba, Kouji Yano
We discuss conditionings to avoid two points and one-point local time penalizations with conditioning to avoid another point, for which we adopt various clocks. We also give correc…
Two-point local time penalizations with various clocks for Lévy processes
Kohki Iba, Kouji Yano
Long-time limit of one-dimensional Lévy processes weighted and normalized with respect to the exponential functional of two-point local times are studied. The limit processes may v…