Fetching the paper…
Reading the bibliography…
We propose and analyse a new Milstein type scheme for simulating stochastic differential equations (SDEs) with highly nonlinear coefficients.
Nonlinear Functional Analysis and its Applications
E. Zeidler · 1985
Earlier work this paper cites.
Introduction to Stochastic Differential Equations
T.C. Gard · 1988
Earlier work this paper cites.
Theory of Martingales
R.S. Liptser and A.N. Shiryayev · 1989
Earlier work this paper cites.
Brownian Motion and Stochastic Calculus
I. Karatzas and S.E. Shreve · 1991
Earlier work this paper cites.
Numerical Solution of Stochastic Differential Equations
P.E. Kloeden and E. Platen · 1992
Earlier work this paper cites.
Testing continuous-time models of the spot interest rate
Y. Ait-Sahalia · 1996
Earlier work this paper cites.
Probability
A.N. Shiryaev · 1996
Earlier work this paper cites.
A simple new formula for options with stochastic volatility
S.L. Heston · 1997
Earlier work this paper cites.
A note on Euler’s approximations
I. Gyöngy · 1998
Earlier work this paper cites.
Balanced implicit methods for stiff stochastic systems
G.N. Milstein, E. Platen, and H. Schurz · 1998
Earlier work this paper cites.
A parametric nonlinear model of term structure dynamics
D.H. Ahn and B. Gao · 1999
Cited alongside, same era.
A-stability and stochastic mean-square stability
D.J. Higham · 2000
Cited alongside, same era.
Option Valuation Under Stochastic Volatility
A.L. Lewis · 2000
Cited alongside, same era.
Mean-square and asymptotic stability of the stochastic theta method
D.J. Higham · 2001
Cited alongside, same era.
Stochastic Numerics for Mathematical Physics. Scientific Computation
G.N. Milstein and M.V. Tretyakov · 2004
Cited alongside, same era.
Convergence and stability of balanced implicit methods for systems of SDEs
H. Schurz · 2005
Cited alongside, same era.
Structure preserving stochastic integration schemes in interest rate derivative modeling
C. Kahl, M. Gunther, and T. Rosberg · 2008
Later among the works it cites.
Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
A. Jentzen, P.E. Kloeden, and A. Neuenkirch · 2009
Later among the works it cites.
A comparison of biased simulation schemes for stochastic volatility models
R. Lord, R. Koekkoek, and D.J.C. Van Dijk · 2009
Later among the works it cites.
Preserving positivity in solutions of discretised stochastic differential equations
J. A. D. Appleby, M. Guzowska, C. Kelly, and A. Rodkina · 2010
Later among the works it cites.
Strong convergence of numerical methods for nonlinear stochastic differential equations under monotone conditions
L. Szpruch and X. Mao · 2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Improved multilevel Monte Carlo convergence using the Milstein scheme
M. Giles · 2006
Cited alongside, same era.
Balanced Milstein methods for ordinary SDEs
C. Kahl and H. Schurz · 2006
Cited alongside, same era.
The improved LaSalle-type theorems for stochastic functional differential equations
Y. Shen, Q. Luo, and X. Mao · 2006
Cited alongside, same era.
Multilevel Monte Carlo path simulation
M.B. Giles · 2008
Cited alongside, same era.
Stochastic volatility models and the pricing of vix options
J. Goard and M. Mazur · 2011
Later among the works it cites.
Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients
M. Hutzenthaler, A. Jentzen, and P.E. Kloeden · 2011
Later among the works it cites.
Numerical simulation of a strongly nonlinear Ait-Sahalia type interest rate model
L. Szpruch, X. Mao, D.J. Higham, and J. Pan · 2011
Later among the works it cites.
Strong convergence of stochastic dissipative systems with super-linear diffusion term
L. Szpruch · 2012
Closest in time.