arXiv subjects
Publications and source records attributed to Yunjiao Hu.
We study the relation between CKLS model and CIR model. We prove that under a suitable transformation, any CKLS model of order $\frac{1}{2}<γ<1$ or $γ> 1$ corresponds to a CIR model under a new probability space. Moreover, we get the explicit solution and the precise distribution of the CKLS model at any time $t$ under the new probability measure. We also give the moment estimation of CKLS model.
Both the mean square polynomial stability and exponential stability of $θ$ Euler-Maruyama approximation solutions of stochastic differential equations will be investigated for each $0\leθ\le 1$ by using an auxiliary function $F$ (see the following definition (2.3)). Sufficient conditions are obtained to ensure the polynomial and exponential stability of the numerical approximations. The results in Liu et al [12] will be improved and generalized to more general cases. Several examples and non stability results are presented to support our conclusions.
Localized sufficient conditions for the large deviation principle of the given stochastic differential equations will be presented for stochastic differential equations with non-Lipschitzian and time-inhomogeneous coefficients, which is weaker than those relevant conditions existing in the literature. We consider at first the large deviation principle when $\int_0^t\sup_{x\in\mathbb{R}^d}||σ(s,x)||\vee|b(s,x)|ds=:C_t<\infty$ for any fixed $t$, then we generalize the conclusion to unbounded case by using bounded approximation program.