Large deviations of sums of independent random variables from the domain of attraction of a stable law

Explicit bivariate rate functions for large deviations in AR(1) and MA(1) processes with Gaussian innovations

“…Since the first establishment of the Large Deviations theory, there has been a great expansion of the number of surveys on Large Deviations Principles (LDP). Nowadays, a variety of examples applied to the time series analysis and stochastic processes are available; for instance, LDPs for stable laws (see, e.g., Heyde [25], Rozovskii [38,39], and Zaigraev [43]), stationary Gaussian processes (see, e.g., Bercu et al [4,5], Bryc and Dembo [10], Donsker and Varadhan [18], and Zani [44]), autoregressive and moving average processes (see, e.g., Bercu [3], Bryc and Smolenski [11], Burton and Dehling [13], Djellout and Guillin [17], Macci and Trapani [30], Mas and Menneteau [32], Miao [34], and Wu [42]) and continuous processes (see, e.g., Bercu and Richou [6,7]).…”

Explicit Bivariate Rate Functions for Large Deviations in AR(1) and MA(1) Processes with Gaussian Innovations

“…Nowadays, we can find a variety of examples applied to the time series analysis and stochastic processes in general; for instance, LDPs for Stable laws (see, e.g. Heyde [22], Rozovskii [31], Rozovskii [32] and Zaigraev [36]), stationary Gaussian processes (see, e.g. Bercu et al [3], Bercu et al [4], Bryc and Dembo [9], Donsker and Varadhan [17] and Zani [37]), autoregressive and moving average processes (see, e.g.…”