Search Advanced

AIMS Mathematics

2019, Volume 4, Issue 5: 1369-1385. doi: 10.3934/math.2019.5.1369
Previous Article Next Article
Research article

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
  • Received: 17 April 2019 Accepted: 28 August 2019 Published: 11 September 2019

  • MSC : 35B27, 35K57, 60F10, 60H15

  • We provide a large deviation principle for jumps and stochastic diffusion processes, according to a viscosity coefficient ($\varepsilon$) and a small scaling parameter ($\delta$) both going at the same rate. To do so we have to come up with estimates on the moment Lyapunov function trajectories.

    Citation: Clement Manga, Alioune Coulibaly, Alassane Diedhiou. On some stochastic differential equations with jumps subject to small positives coefficients[J]. AIMS Mathematics, 2019, 4(5): 1369-1385. doi: 10.3934/math.2019.5.1369

    Related Papers:

  • We provide a large deviation principle for jumps and stochastic diffusion processes, according to a viscosity coefficient ($\varepsilon$) and a small scaling parameter ($\delta$) both going at the same rate. To do so we have to come up with estimates on the moment Lyapunov function trajectories.


    加载中


    [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.
  • Reader Comments
  • © 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
AIMS Mathematics
1.8 3.4

Metrics

Article views(3818) PDF downloads(368) Cited by(0)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog