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Abstract
In this paper, we consider a multiplicative Poisson shot noise process with compensation which converges weakly to a fractional Brownian motion. Under mild conditions, the sample path large deviations for this process are established under the uniform topology. The methods include the weak convergence techniques, exponentially good approximation and exponential inequalities
Acknowledgments
The authors would like to express great gratitude to the two anonymous referees and the associate editor for the careful reading and constructive comments which led to an improved presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the author(s).
Additional information
Funding
Hui JIANG is supported by National Natural Science Foundation of China [grant number 11771209], Qingshan YANG is supported by National Natural Science Foundation of China [grant numbers 11401090, 11971097 and 11971098] and the Fundamental Research Funds for the Central Universities [grant number 2412019FZ031].