In this paper, we study the asymptotic behavior of randomly perturbed Chan–Karolyi–Longstaff–Sanders (CKLS) model with small parameter ε. When ε→0, the central limit theorem and moderate deviation principle for the solution of randomly perturbed CKLS model are obtained.

Applying the large deviations and moderate deviations for the log-likelihood ratio of the Jacobi model, we give negative regions in testing Jacobi model, and get the decay rates of the error probabilities.

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.

We obtain the rate of convergence of the functional limit for increments of a d-dimensional Brownian motion. As an application of the main result, we get a d-dimensional version of the result on the size of small increments of a Brownian motion.

We study moderate deviations for maximum likelihood estimators of parameters in generalized squared radial Ornstein-Uhlenbeck processes. The moderate deviation principles of the two parameters are established.

In this paper, we obtain a moderate deviation result for the maximum likelihood estimator under certain regular conditions. Two examples of non-regular cases are studied.

In this article, we consider the problem of the minimal entropy martingale measure of a jump process influenced by jump times. The minimal entropy martingale measure of the price process is given out by the exponential martingale method, and the expression of the corresponding relative entropy...

The two-parameter Poisson-Dirichlet distribution is the law of a sequence of decreasing nonnegative random variables with total sum one. It can be constructed from stable and gamma subordinators with the two parameters, [alpha] and [theta], corresponding to the stable component and the gamma...

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...