Unbalanced multi-drawing urn with random addition matrix II
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 m balls, say k white balls and m−k black balls. We
inspect the colours and then we return the balls, according to a predefined
replacement matrix, together with (m − k) Xn white balls and k Yn black
balls. Here, we extend the classical assumption that the random variables
(Xn, Yn) are bounded and i.i.d. We prove a strong law of large numbers and
a central limit theorem on the proportion of white balls for the total number
of balls after n draws under the following more general assumptions: (i) a
finite second-order moment condition in the i.i.d. case; (ii) regular variation
type for the first and second moments in the independent case.
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…