24 citations · 59 across the 23 of their papers we have counts for
17 papers · 1 filter
Are random random walks normal?
Kais Hamza, Laurent Tournier
Given a symmetric simple random walk , the family of all symmetric simple random walks adapted to the filtration of was studied…
Brownian symmetrization of planar domains
Maher Boudabra, Kais Hamza
One of aims of this note is to capture the interest of the mathematical community to a novel transformation, which we shall call Brownian symmetrization. This transformation arises…
Long range one-cookie random walk with positive speed
Andrea Collevecchio, Kais Hamza, Tuan-Minh Nguyen
We study one-dimensional excited random walks with non-nearest neighbor jumps. When the process is at a vertex that has not been visited before, its next transition has a positive…
Limit theorems and ergodicity for general bootstrap random walks
A. Collevecchio, K. Hamza, M. Shi +1
Given the increments of a simple symmetric random walk , we characterize all possible ways of recycling these increments into a simple symmetric random walk $(Y_n)_{…
Matching marginals and sums
Robert Griffiths, Kais Hamza
For a given set of random variables we seek as large a family as possible of random variables such that the marginal laws and the laws of the sums…
A deterministic walk on the randomly oriented Manhattan lattice
Andrea Collevecchio, Kais Hamza, Laurent Tournier
Consider a randomly-oriented two dimensional Manhattan lattice where each horizontal line and each vertical line is assigned, once and for all, a random direction by flipping indep…
Limit theorems for multi-type general branching processes with population dependence
Jie Yen Fan, Kais Hamza, Peter Jagers +1
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition…
Persistence of Small Noise and Random initial conditions
J. Baker, P. Chigansky, K. Hamza +1
The effect of small noise in a smooth dynamical system is negligible on any finite time interval. Here we study situations when it persists on intervals increasing to infinity. Suc…
Invariance principle for biased Boostrap Random Walk
Andrea Collevecchio, Kais Hamza, Yunxuan Liu
Our main goal is to study a class of processes whose increments are generated via a cellular automata rule. Given the increments of a simple biased random walk, a new sequence of (…
Convergence of the age structure of general schemes of population processes
Jie Yen Fan, Kais Hamza, Peter Jagers +1
We consider a family of general branching processes with reproduction parameters depending on the age of the individual as well as the population age structure and a parameter ,…
Attraction properties for general urn processes and applications to a class of interacting reinforced particle systems
Jiro Akahori, Andrea Collevecchio, Timothy Garoni +1
We study a system of interacting reinforced random walks defined on polygons. At each stage, each particle chooses an edge to traverse which is incident to its position. We allow t…
Bootstrap Random Walks
Andrea Collevecchio, Kais Hamza, Meng Shi
Consider a one dimensional simple random walk . We form a new simple symmetric random walk by taking sums of products of the increments of …
Escape from the boundary in Markov population processes
A. D. Barbour, Kais Hamza, Haya Kaspi +1
Density dependent Markov population processes in large populations of size were shown by Kurtz (1970, 1971) to be well approximated over finite time intervals by the solution o…
The mixing advantage is less than 2
Kais Hamza, Peter Jagers, Aidan Sudbury +1
Corresponding to independent non-negative random variables , are values , where each is the expected value of the maximum of independent cop…
A Family of non-Gaussian Martingales with Gaussian Marginals
kais Hamza, Fima C. Klebaner
We construct a family of non-Gaussian martingales the marginals of which are all Gaussian. We give the predictable quadratic variation of these processes and show they do not have…
On Solutions of First Order Stochastic Partial Differential Equations
K. Hamza, F. C. Klebaner
This note is concerned with an important for modelling question of existence of solutions of stochastic partial differential equations as proper stochastic processes, rather than p…
On nonexistence of non-constant volatility in the Black-Scholes formula
K. Hamza, F. C. Klebaner
We prove that if the Black-Scholes formula holds with the spot volatility for call options with all strikes, then the volatility parameter is constant. The proof relies some result…