24 citations · 98 across the 27 of their papers we have counts for
8 papers · 1 filter
Uniform Lorden-type bounds for overshoot moments for standard exponential families: small drift and an exponential correction
El'mira Yu. Kalimulina, Mark Ya. Kelbert
We study the overshoot \(R_b=S_{τ(b)}-b\) of a random walk with independent identically distributed increments from a standardised one-parameter exponential family, with primary em…
On the occupancy problem for a regime switching model
Michael Grabchak, Mark Kelbert, Quentin Paris
This article studies the expected occupancy probabilities on an alphabet. Unlike the standard situation, where observations are assumed to be independent and identically distribute…
Weighted entropy: basic inequalities
Mark Kelbert, Izabella Stuhl, Yuri Suhov
This paper represents an extended version of an earlier note [10]. The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-depe…
Weighted entropy and optimal portfolios for risk-averse Kelly investments
Mark Kelbert, Izabella Stuhl, Yuri Suhov
Following a series of works on capital growth investment, we analyse log-optimal portfolios where the return evaluation includes `weights' of different outcomes. The results are tw…
Asymptotic behaviour of non-isotropic random walks with heavy tails
Mark Kelbert, Enzo Orsingher
A random flight on a plane with non-isotropic displacements at the moments of direction changes is considered. In the case of exponentially distributed flight lengths a Gaussian li…
Weak Error for Continuous Time Markov Chains Related to Fractional in Time P(I)DEs
M. Kelbert, V. Konakov, S. Menozzi
We provide sharp error bounds for the difference between the transition densities of some multidimensional Continuous Time Markov Chains (CTMC) and the fundamental solutions of som…