A joint large deviation principle for G-Brownian motion and its quadratic variation process is presented. The rate function is not a quadratic form due to quadratic variation uncertainty. A large deviation principle for stochastic differential equations driven by G-Brownian motion is also...

Sample path large and moderate deviation principles for Markov modulated risk models with delayed claims are proved by the exponential martingale method. As applications, asymptotic estimates and exponential bounds of the ruin probability are also studied.

In this paper, we obtain the moderate deviation principle for a sequence of Brownian motions defined on the unit sphere in Rd by using the cumulant method introduced by  Puhalskii (1994b) and generalize it to Ornstein–Uhlenbeck processes taking values on the unit sphere in Rd.

Let fn(x) be the non-parametric kernel density estimator of a density function f(x) based on a kernel function K. In this paper, we first prove two moderate deviation theorems in for {fn(x),n=1}. Then, as an application of the moderate deviations, we obtain a law of the iterated logarithm for...

We study pathwise properties and homeomorphic property with respect to the initial values for stochastic differential equations driven by G-Brownian motion. We first present a Burkholder-Davis-Gundy inequality and an extension of Itô's formula for the G-stochastic integrals. Some moment...