A Generalized Urn with Multiple Drawing and Random Addition
Olfa, Aguech Rafik, Lasmar Nabil, Selmi . 2018
In this paper, we consider an unbalanced urn model with multiple drawing. At each
discrete time step n, we draw m balls at random from an urn containing white and blue
balls. The replacement of the balls follows either opposite or self-reinforcement rule.
Under the opposite reinforcement rule, we use the stochastic approximation algorithm to
obtain a strong law of large numbers and a central limit theorem for Wn: the number of
white balls after n draws. Under the self reinforcement rule, we prove that, after suitable
normalization, the number of white balls Wn converges almost surely to a random variable
W1 which has an absolutely continuous distribution.
In this paper, we consider a two-dimension symmetric random walk with reset. We give, in the first part, some results about the distribution of every component. In the second part, we give some…
In this paper, we give some results about a multi-drawing urn with random
addition matrix. The process that we study is described as: at stage n ≥ 1,
we pick out at random…
I
In this article, we consider several models of random walks in one or several
dimensions, additionally allowing, at any unit of time, a reset (or “catastrophe”) of
the walk…