### Basak Gever (TOBB University of Economics and Technology, Ankara, Turkey)

#### Weak convergence theorem for a random walk with generalized reflecting barrier

*Wednesday 19 October 2016 at 15.00, JCMB 5215*

##### Abstract

In this work, a stochastic process with discrete interference of chance and
generalized reflecting barrier (X (t)) is constructed and the ergodicity of
this process is proved. Using basic identity for random walk processes, a
characteristic function of the ergodic distribution is written with the help
of characteristics of the boundary functional S_(N_1(x)). Moreover, a weak
convergence theorem for the ergodic distribution of the standardized process
Y_λ(t) = X(t)/λ is proved, as λ → ∞ and the limit form of the ergodic
distribution is found.

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