Sample path large deviations for the multiplicative Poisson shot noise process with compensation

References

• P. Billingsley, Convergence of Probability Measures, Wiley, New York, 1999.
   Google Scholar
• N.H. Bingham, C.M. Goldie, and J.L. Teugels, Regular Variation, Cambridge University Press, Cambridge, 1987.
   Google Scholar
• M. Boué and P. Dupuis, A variational representation for certain functionals of Brownian motion, Ann. Probab. 26(4) (1998), pp. 1641–1659. doi: 10.1214/aop/1022855876
   Web of Science ®Google Scholar
• A. Budhiraja, P. Dupuis, and V. Maroulas, Variational representation for continuous time processes, Ann. de l'Institut Henri Poincaré (B) Probab. Stat. 47 (2011), pp. 725–747. doi: 10.1214/10-AIHP382
   Web of Science ®Google Scholar
• A. Budhiraja, P. Dupuis, and A. Ganguly, Large deviations for small noise diffusions in a fast Markovian environment, Electron. J. Probab. 11 (2018), pp. 1–33.
   Google Scholar
• A. Budhiraja, W.T. Fan, and R.Y. Wu, Large deviations for Brownian particle systems with killing, J. Theore. Probab. 31(3) (2018), pp. 1779–1818. doi: 10.1007/s10959-017-0764-2
   Web of Science ®Google Scholar
• A. Budhiraja and P. Nyquist, Large deviations for multidimensional state-dependent shot-noise processes, J. Appl. Probab. 52(4) (2015), pp. 1097–1114. doi: 10.1239/jap/1450802755
   Web of Science ®Google Scholar
• A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications, Springer-Verlag, New York, 1998.
   Google Scholar
• Z. Dong, J.L. Zhai, and R.R. Zhang, Large deviation principles for 3D stochastic primitive equations, J. Differ. Equ. 263(5) (2017), pp. 3110–3146. doi: 10.1016/j.jde.2017.04.025
   Web of Science ®Google Scholar
• K.R. Duffy and G.L. Torrisi, Sample path large deviations of Poisson shot noise with heavy-tailed semiexponential distributions, J. Appl. Probab. 48 (2011), pp. 688–698. doi: 10.1017/S002190020000824X
   Web of Science ®Google Scholar
• P. Dupuis and Y. Liu, On the large deviation rate function for the empirical measures of reversible jump Markov processes, Ann. Probab. 43(3) (2015), pp. 1121–1156. doi: 10.1214/13-AOP883
   Web of Science ®Google Scholar
• P. Dupuis and D. Lipschutz, Large deviations for the empirical measure of a diffusion via weak convergence methods, Stoch. Process. Appl. 128 (2018), pp. 2581–2604. doi: 10.1016/j.spa.2017.09.020
   Web of Science ®Google Scholar
• J. Feng, T.G. Kurtz, Large Deviations for Stochastic Processes, Mathematical Surveys and Monographs Vol. 131, American Mathematical Society, 2006. https://link.springer.com/article/10.1007/s10959-007-0136-4.
   Google Scholar
• A. Ganesh, C. Macci, and G.L. Torrisi, Sample path large deviations principles for Poisson shot noise processes, and applications, Electron. J. Probab. 10 (2005), pp. 1026–1043. doi: 10.1214/EJP.v10-273
   Web of Science ®Google Scholar
• A. Ganesh and G.L. Torrisi, A class of risk processes with delayed claims: Ruin probability estimates under heavy tail conditions, J. Appl. Probab. 43 (2006), pp. 916–926. doi: 10.1239/jap/1165505197
   Web of Science ®Google Scholar
• Y. Hu and B. Øksendal, Fractional white noise calculus and applications to finance, Infinite Dimensional Anal. Q. Probab. Rel. Top. 6 (2003), pp. 1–32. doi: 10.1142/S0219025703001110
   Web of Science ®Google Scholar
• C. Klüppelberg and T. Mikosch, Delay in claim settlement and ruin probability approximations, Scand. Actuar. J. 1995 (1995), pp. 154–168. doi: 10.1080/03461238.1995.10413955
   Google Scholar
• C. Klüppelberg and T. Mikosch, Explosive Poisson shot noise processes with applications to risk reserves, Bernoulli 1 (1995), pp. 125–147. doi: 10.2307/3318683
   Google Scholar
• C. Klüppelberg, T. Mikosch, and A. Schärf, Regular variation in the mean and stable limits for Poisson shot noise, Bernoulli 9 (2003), pp. 467–496. doi: 10.3150/bj/1065444814
   Web of Science ®Google Scholar
• C. Klüppelberg and C. Kühn, Fractional Brownian motion as a weak limit of Poisson shot noise processes-with applications to finance, Stoch. Process. Appl. 113 (2004), pp. 333–351. doi: 10.1016/j.spa.2004.03.015
   Web of Science ®Google Scholar
• J.A. Lane, The central limit theorem for the Poisson shot-noise process, J. Appl. Probab. 21 (1984), pp. 287–301. doi: 10.2307/3213640
   Web of Science ®Google Scholar
• R. Lund, W.P. Mccormick, and Y.H. Xiao, Limiting properties of Poisson shot noise processes, J. Appl. Probab. 41 (2004), pp. 911–918. doi: 10.1239/jap/1091543433
   Web of Science ®Google Scholar
• C. Macci and G.L. Torrisi, Asymptotic results for perturbed risk processes with delayed claims, Insur.: Math. Econ. 34 (2004), pp. 307–320.
   Web of Science ®Google Scholar
• C. Macci, G. Stabile, and G.L. Torrisi, Lundberg parameters for non standard risk processes, Scand. Actuar. J. 2005 (2005), pp. 417–432. doi: 10.1080/03461230500363048
   Google Scholar
• C. Macci and G.L. Torrisi, Risk process with shot noise Cox claim number process and reserve dependent premium rate, Insur.: Math. Econ. 48 (2011), pp. 134–145.
   Web of Science ®Google Scholar
• J.G. Ren, S.Y. Xu, and X.C. Zhang, Large deviations for multivalued stochastic differential equations, J. Theor. Probab. 23(4) (2010), pp. 1142–1156. doi: 10.1007/s10959-009-0274-y
   Web of Science ®Google Scholar
• G. Stabile and G.L. Torrisi, Large deviations of Poisson shot noise processes under heavy tail semi-exponential conditions, Stat. Probab. Lett. 80 (2010), pp. 1200–1209. doi: 10.1016/j.spl.2010.03.017
   Web of Science ®Google Scholar
• G.L. Torrisi, Simulating the ruin probability of risk processes with delay in claim settlement, Stoch. Process. Appl. 112 (2004), pp. 225–244. doi: 10.1016/j.spa.2004.02.007
   Web of Science ®Google Scholar
• C.G. Weng, Y. Zhang, and K.S. Tan, Tail behavior of Poisson shot noise processes under heavy-tailed shocks and actuarial applications, Meth. Comput. Appl. Probab. 15 (2013), pp. 655–682. doi: 10.1007/s11009-011-9274-3
   Web of Science ®Google Scholar
• J. Yan and F.Q. Gao, Exponential martingale and large deviations for a Cox risk process with Poisson shot noise intensity, J. Math. Anal. Appl. 394 (2012), pp. 74–83. doi: 10.1016/j.jmaa.2012.04.052
   Web of Science ®Google Scholar
• J.L. Zhai and T.S. Zhang, Large deviations for 2-D stochastic Navier-Stokes equations driven by multiplicative Lévy noises, Bernoulli 21 (2015), pp. 2351–2392. doi: 10.3150/14-BEJ647
   Web of Science ®Google Scholar