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Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient.
Undamped oscillations derived from the law of mass action
Lotka, A. J · 1920
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LXXXVIII. On “relaxation-oscillations”
van der Pol, B · 1926
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Fluctuations in the abundance of a species considered mathematically
Volterra, V · 1926
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On the theory of superconductivity
Ginzburg, V. L., and Landau, L. D · 1950
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Continuous Markov processes and stochastic equations
Maruyama, G · 1955
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Determinisitic nonperiodic flow
Lorenz, E · 1963
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Symmetry breaking instabilities in dissipative systems ii
Prigogine, I., and Lefever, R · 1968
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Some further studies of nonlinear oscillations in chemical systems
Tyson, J. J · 1973
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Approximate integration of stochastic differential equations
Milstein, G. N · 1974
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Toward an understanding of stochastic Hopf bifurcation: a case study
Arnold, L., Sri Namachchivaya, N., and Schenk-Hoppé, K. R · 1975
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Population biology of infectious diseases: Part I
Anderson, R., and May, R · 1979
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Galerkin approximation of nonlinear Markov processes
Dawson, D. A · 1981
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A theory of the term structure of interest rates
Cox, J. C., Ingersoll, J. J. E., and Ross, S. A · 1985
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A theoretical model of phase transitions in human hand movements
Haken, H., Kelso, J. A. S., and Bunz, H · 1985
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Periodic behavior of the stochastic Brusselator in the mean-field limit
Scheutzow, M · 1986
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A stochastic theory of phase transitions in human hand movements
Schöner, G., Haken, H., and Kelso, J. A. S · 1986
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Numerical integration of stochastic differential equations
Milstein, G. N · 1988
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A simple proof of the existence of a solution to the Itô equation with monotone coefficients
Krylov, N. V · 1990
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Stochastic equations in infinite dimensions
Da Prato, G., and Zabczyk, J · 1992
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Numerical solution of stochastic differential equations
Kloeden, P. E., and Platen, E · 1992
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A closed-form solution for options with stochastic volatility with applications to bond and currency options
Heston, S. L · 1993
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Stochastic transient of a noisy von der Pol oscillator
Leung, H · 1995
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Testing continuous-time models of the spot interest rate
Ait-Sahalia, Y · 1996
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Existence of strong solutions for Itô’s stochastic equations via approximations
Gyöngy, I., and Krylov, N · 1996
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Semi-implicit Euler-Maruyama scheme for stiff stochastic equations
Hu, Y · 1996
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Exponential convergence of Langevin distributions and their discrete approximations
Roberts, G. O., and Tweedie, R. L · 1996
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Bifurcation scenarios of the noisy Duffing-van der Pol oscillator
Schenk-Hoppé, K. R · 1996
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The random attractor of the stochastic lorenz system
Schmalfuß, B · 1997
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Random dynamical systems
Arnold, L · 1998
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A note on Euler’s approximations
Gyöngy, I · 1998
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Balanced implicit methods for stiff stochastic systems
Milstein, G. N., Platen, E., and Schurz, H · 1998
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Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II
Gyöngy, I · 1999
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Option valuation under stochastic volatility
Lewis, A. L · 2000
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Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?
Timmer, J., Haussler, S., Lauk, M., and Lucking, C.-H · 2000
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Infinite-dimensional quadrature and approximation of distributions
Creutzig, J., Dereich, S., Müller-Gronbach, T., and Ritter, K · 2009
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Pathwise numerical approximations of SPDEs with additive noise under non-global Lipschitz coefficients
Jentzen, A · 2009
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Pathwise approximation of stochastic differential equations on domains: higher order convergence rates without global Lipschitz coefficients
Jentzen, A., Kloeden, P. E., and Neuenkirch, A · 2009
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Modeling complex systems
Boccara, N · 2010
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Two-sided error estimates for the stochastic theta method
Beyn, W.-J., and Kruse, R · 2010
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Multi-level Monte Carlo algorithms for infinite-dimensional integration on ℝ N \mathbb{R}^{N}
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Multilevel Monte Carlo methods
Heinrich, S · 2001
Cited alongside, same era.
On the discretization in time of parabolic stochastic partial differential equations
Printems, J · 2001
Cited alongside, same era.
Strong convergence of Euler-type methods for nonlinear stochastic differential equations
Higham, D. J., Mao, X., and Stuart, A. M · 2002
Cited alongside, same era.
Ergodicity for SDEs and approximations: locally Lipschitz vector fields and degenerate noise
Mattingly, J. C., Stuart, A. M., and Higham, D. J · 2002
Cited alongside, same era.
The Euler scheme with irregular coefficients
Yan, L · 2002
Cited alongside, same era.
General theorems for numerical approximation of stochastic processes on the Hilbert space H 2 ( [ 0 , T ] , μ , ℝ d ) H_{2}([0,T],\mu,\mathbb{R}^{d})
Schurz, H · 2003
Cited alongside, same era.
Hickernell, F. J., Müller-Gronbach, T., Niu, B., and Ritter, K · 2010
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SPDE in Hilbert space with locally monotone coefficients
Liu, W., and Röckner, M · 2010
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Stochastic ordinary differential equations in applied and computational mathematics
Higham, D. J · 2011
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Convergence of the stochastic Euler scheme for locally Lipschitz coefficients
Hutzenthaler, M., and Jentzen, A · 2011
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Strong and weak divergence in finite time of Euler’s method for stochastic differential equations with non-globally Lipschitz continuous coefficients
Hutzenthaler, M., Jentzen, A., and Kloeden, P. E · 2011
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Kruse, R · 2011
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Numerical simulation of a strongly nonlinear Ait-Sahalia-type interest rate model
Szpruch, L., Mao, X., Higham, D. J., and Pan, J · 2011
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Multilevel Monte Carlo method for parabolic stochastic partial differential equations
Barth, A., Lang, A., and Schwab, C · 2012
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Nonasymptotic mixing of the MALA algorithm
Bou-Rabee, N., and Hairer, M · 2012
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Cox, S. G., and van Neerven, J. M. A. M · 2012
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Semigroup splitting and cubature approximations for the stochastic Navier-Stokes equations
Doersek, P · 2012
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An Euler-type method for the strong approximation of the Cox-Ingersoll-Ross process
Dereich, S., Neuenkirch, A., and Szpruch, L · 2012
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Extinction in neutrally stable stochastic Lotka-Volterra models
Dobrinevski, A., and Frey, E · 2012
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Strong convergence of an explicit numerical method for SDEs with non-globally Lipschitz continuous coefficients
Hutzenthaler, M., Jentzen, A., and Kloeden, P. E · 2012
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Taylor Approximations for Stochastic Partial Differential Equations
Jentzen, A., and Kloeden, P · 2012
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Finite-element-based discretizations of the incompressible Navier-Stokes equations with multiplicative random forcing
Brzeźniak, Z., Carelli, E., and Prohl, A · 2013
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The tamed Milstein method for commutative stochastic differential equations with non-globally Lipschitz continuous coefficients
Gan, S., and Wang, X · 2013
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Loss of regularity for Kolmogorov equations
Hairer, M., Hutzenthaler, M., and Jentzen, A · 2013
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Divergence of the multilevel Monte Carlo Euler method for nonlinear stochastic differential equations
Hutzenthaler, M., Jentzen, A., and Kloeden, P. E · 2013
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Local and global well-posedness of SPDE with generalized coercivity conditions
Liu, W., and Röckner, M · 2013
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Strong convergence and stability of implicit numerical methods for stochastic differential equations with non-globally Lipschitz continuous coefficients
Mao, X., and Szpruch, L · 2013
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Strong convergence rates for backward Euler-Maruyama method for nonlinear dissipative-type stochastic differential equations with super-linear diffusion coefficients
Mao, X., and Szpruch, L · 2013
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