Under an appropriate ISS condition, it is shown that global adaptive stabilization of a class of cascade systems with nonlinear parameterization is achievable by non-Lipschitz continuous partial-state adaptive regulator. This result complements the earlier work [10] on adaptive control of uncertain nonlinear systems with uncontrollable unstable linearization, which are impossible to be dealt wi...

In this paper, we continue in solving reflected generalized backward stochastic differential equations (RGBSDE for short) and fixed terminal time with use some new technical aspects of the stochastic calculus related to the reflected generalized BSDE. Here, existence and uniqueness of solution is proved under the non-Lipschitz condition on the coefficients.

We consider an inverse problem of determining a spatially varying factor in a source term in a nonstationary linearized Navier-Stokes equations by observation data in an arbitrarily fixed sub-domain over some time interval. We prove the Lipschitz stability provided that the t-dependent factor satisfies a non-degeneracy condition. Our proof based on a new Carleman estimate for the Navier-Stokes ...

We obtain sufficient condition for SDEs to evolve in the positive orthrant. We use comparison theorem arguments to achieve this. As a result we prove the existence of a unique strong solution for a class of multidimensional degenerate SDEs with non-Lipschitz diffusion coefficients.

In this paper, we study a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) that has non-Lipschitz generator and unbounded random time horizon. For any p ∈ (1,∞), we show that the BSDEJ with a p-integrable terminal condition admits a unique L-type solution.

Keywords: Stochastic differential delay equation (SDDE) Split-step theta scheme Stochastic linear theta scheme Strong convergence rate Exponential mean square stability a b s t r a c t This paper establishes the boundedness, convergence and stability of the two classes of theta schemes, namely split-step theta (SST) scheme and stochastic linear theta (SLT) scheme, for stochastic differential de...

A new explicit stochastic scheme of order 1 is proposed for solving commutative differential equations (SDEs) with non-globally Lipschitz continuous coefficients. The method a semi-tamed version Milstein to solve SDEs the drift coefficient consisting non-Lipschitz term and globally term. It easily implementable achieves higher strong convergence order. stability criterion this derived, which sh...