AIMS Mathematics, 2019, 4(5): 1369-1385. doi: 10.3934/math.2019.5.1369

Research article

Export file:

Format

• RIS(for EndNote,Reference Manager,ProCite)
• BibTex
• Text

Content

• Citation Only
• Citation and Abstract

On some stochastic differential equations with jumps subject to small positives coefficients

Laboratory of Mathematics and Applications, UFR Sciences & Technologies, University of Assane SecK, UASZ, BP 523, Ziguinchor, Senegal

## Abstract    Full Text(HTML)    Figure/Table    Related pages

We provide a large deviation principle for jumps and stochastic diffusion processes, according to a viscosity coefficient (ε) and a small scaling parameter (δ) both going at the same rate. To do so we have to come up with estimates on the moment Lyapunov function trajectories.
Figure/Table
Supplementary
Article Metrics

# References

1. P. Baldi, Large deviations for diffusions processes with homogenization applications, Ann. Probab., 19 (1991), 509–524.

2. P. H. Baxendale, D. W. Stoock, Large deviations and stochastic flows of diffeomorphisms, Probab. Th. Rel. Fields, 80 (1988), 169–215.

3. D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, 2009.

4. C. Manga, A. Coulibaly, A. Diedhiou, On jumps stochastic evolution equations with application of homogenization and large deviations, J. Math. Res., 11 (2019), 125–134.

5. A. Dembo, O. Zeitouni, Large Deviations Techniques and Applications, Boston: Jones and Bartlett, 1998.

6. J. Feng, T. G. Kurtz, Large Deviations for Stochastic Processes, Providence: American Mathematical Society, 2006.

7. J. Kueibs, W. V. Li, W. Linde, The gaussian measure of shifted balls, Probab. Th. Rel. Fields, 98 (1994), 143–162.

8. M. I. Freidlin, Functional Integration and Partial Differential Equations, Princeton: Princeton University Press, 1985.

9. M. I. Freidlin, R. B. Sowers, A comparison of homogenization and large deviations, with applications to wavefront propagation, Stoch. Proc. Appl., 82 (1999), 23–52.

10. N. Ikeda, S. Watanabe, Stochastic Differential Equations and Diffusion Processes, Elsevier, 2014.

11. E. Pardoux, Yu. Veretennikov, On the Poisson equation and diffusion approximation, I. Ann. Probab., 29 (2001), 1061–1085.

12. M. Röckner, T. Zhang, Stochastic evolution equations of jump type: Existence, uniqueness and large deviation principles, T. Potential Anal., 26 (2007), 255–279.

13. S. R. S. Varadhan, Large Deviations and Applications, Philadelphia: Society for Industrial and Applied Mathematics, 1984.

14. A. W. van der Vaart, J. H. van Zanten, Rates of contraction of posterior distributions based on Gaussian process priors, Ann. Statist., 36 (2008), 1435–1463.

15. H. Y. Zhao, S. Y. Xu, Freidlin-Wentzell's large deviations for stochastic evolution equations with Poisson jumps, Adv. Pure Math., 6 (2016), 676–694.