Renewal theorems and stability for the reflected process

Renewal Theorems and Stability for the Reflected Process

Renewal-like results and stability theorems relating to the largetime behaviour of a random walk Sn reflected in its maximum, Rn = max0≤j≤n Sj − Sn, are proved. Mainly, we consider the behaviour of the exit time, τ(r), where τ(r) = min{n ≥ 1 : Rn > r}, r > 0, and the exit position, Rτ(r), as r grows large, with particular reference to the cases when Sn has finite variance and/or finite mean. Th...

Renewal Theorems for Markov Chains

Limit Theorems for Renewal Processes

This article describes the Key renewal theorem and the Blackwell’s renewaltheorem. These two limit theorems for renewal processes are equivalent but of different forms.They are particularly useful for characterizing the asymptotic behavior of a probabilisticquantity of interest in a renewal process. We present two applications of these limit theorems:the limiting distributions o...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

Some Blackwell-type Renewal Theorems for Weighted Renewal Functions

In this paper, a new approach is proposed to investigate Blackwell-type renewal theorems for weighted renewal functions systematically according to which of the tails of weighted renewal constants or the underlying distribution is asymptotically heavier. Some classical results are improved considerably.