Projects per year
In this article we introduce a number of explicit schemes, which are amenable to Khasminski’s technique and are particularly suitable for highly nonlinear stochastic differential equations (SDEs). We show that without additional restrictions to those which guarantee the exact solutions possess their boundedness in expectation with respect to certain Lyapunov-type functions, the numerical solutions converge strongly to the exact solutions in finite-time. Moreover, based on the convergence theorem of nonnegative semimartingales, positive results about the ability of the explicit numerical scheme proposed to reproduce the well-known LaSalle-type theorem of SDEs are proved here, from which we deduce the asymptotic stability of numerical solutions. Some examples are discussed to demonstrate the validity of the new numerical schemes and computer simulations are performed to support the theoretical results.
- stochastic differential equations
- local Lipschitz condition
- explicit scheme
- Lyapunov functions
- LaSalle's theorem
- strong convergence
FingerprintDive into the research topics of 'Strong convergence and asymptotic stability of explicit numerical schemes for nonlinear stochastic differential equations'. Together they form a unique fingerprint.
1/10/16 → 30/09/21
Ergodicity and invariant measures of stochastic delay systems driven by various noises and their applications (Prof. Fuke Wu)
16/03/17 → 15/06/20
Project: Research Fellowship
1/10/12 → 30/09/16
Project: Research - Studentship