# Large deviation principles for renewal-reward processes

@inproceedings{Zamparo2021LargeDP, title={Large deviation principles for renewal-reward processes}, author={Marco Zamparo}, year={2021} }

We establish a sharp large deviation principle for renewal-reward processes, supposing that each renewal involves a broad-sense reward taking values in a real separable Banach space. In fact, we demonstrate a weak large deviation principle without assuming any exponential moment condition on the law of waiting times and rewards by resorting to a sharp version of Cramér’s theorem. We also exhibit sufficient conditions for exponential tightness of renewal-reward processes, which leads to a full…

## References

SHOWING 1-10 OF 28 REFERENCES

### Functional large deviation principles for first-passage-time processes

- Mathematics
- 1997

We apply an extended contraction principle and superexponential con- vergence in probability to show that a functional large deviation principle for a sequence of stochastic processes implies a…

### Large deviation principles for the finite-dimensional distributions of compound renewal processes

- Mathematics
- 2015

The paper deals with the large deviation probabilities for compound renewal processes. We establish the local and “integral” principles of large deviations in the state space of the process (i.e. for…

### Large deviation results for compound Markov renewal processes

- Mathematics
- 2005

In this paper we present some large deviation results for com- pound Markov renewal processes. We start studying the exponential decay of level crossing probabilities as the level goes to infinity.…

### Large deviations behavior of counting processes and their inverses

- MathematicsQueueing Syst. Theory Appl.
- 1994

It is shown that embedded regenerative structure is sufficient for the counting process or its inverse process to have exponential asymptotics, and thus satisfy the Gärtner-Ellis condition.

### Large Deviation Principles for Trajectories of Compound Renewal Processes. I

- Mathematics
- 2016

The present paper continues studies of large deviation principles for compound renewal processes that were started in [A. A. Borovkov, Asymptotic Analysis of Random Walking. Fast Decreasing Increment…

### Large deviations of inverse processes with nonlinear scalings

- Mathematics
- 1998

We show, under regularity conditions, that a nonnegative nondecreas- ing real-valued stochastic process satis(cid:12)es a large deviation principle (LDP) with nonlinear scaling if and only if its…

### Large deviations in renewal models of statistical mechanics

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2019

In Zamparo (2019 (arXiv:1903.03527)) the author has recently established sharp large deviation principles for cumulative rewards associated with a discrete-time renewal model, supposing that each…