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We develope a perturbation theory for stochastic differential equations (SDEs) by which we mean both stochastic ordinary differential equations (SODEs) and stochastic partial differential equations (SPDEs).
Stochastic flows and Bismut formulas for stochastic Hamiltonian systems
Zhang, X · 1949
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Monotone (nonlinear) operators in Hilbert space
Minty, G. J · 1962
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on a “monotonicity” method for the solution of non-linear equations in Banach spaces
Minty, G. J · 1963
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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 · 1966
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Équations aux dérivées partielles stochastiques de type monotone
Pardoux, É · 1975
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Semilinear stochastic evolution equations: boundedness, stability and invariant measures
Ichikawa, A · 1984
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On some stability properties of stochastic differential equations of Itô’s type
Maslowski, B · 1986
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Stochastic equations in infinite dimensions
Da Prato, G., and Zabczyk, J · 1992
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Lyapunov-type conditions for stationary distributions of diffusion processes on Hilbert spaces
Leha, G., and Ritter, G · 1994
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Strong p p -completeness of stochastic differential equations and the existence of smooth flows on noncompact manifolds
Li, X.-M · 1994
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Stochastic Cahn-Hilliard equation
Da Prato, G., and Debussche, A · 1996
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Semi-implicit Euler-Maruyama scheme for stiff stochastic equations
Hu, Y · 1996
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Deterministic and stochastic Duffing-van der Pol oscillators are non-explosive
Schenk-Hoppé, K. R · 1996
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Monte Carlo complexity of global solution of integral equations
Heinrich, S · 1998
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Effect of stochastic forcing on the Duffing oscillator
Datta, S., and Bhattacharjee, J. K · 2001
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On the discretization in time of parabolic stochastic partial differential equations
Printems, J · 2001
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Strong convergence of Euler-type methods for nonlinear stochastic differential equations
Higham, D. J., Mao, X., and Stuart, A. M · 2002
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Dynamics of evolutionary equations
Sell, G. R., and You, Y · 2002
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Lyapunov functions and stationary distributions of stochastic evolution equations
Leha, G., and Ritter, G · 2003
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Convergence of the spectral method for stochastic Ginzburg-Landau equation driven by space-time white noise
Liu, D · 2003
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Stochastische Analysis mit Finanzmathematik
Kühn, C · 2004
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On discretization schemes for stochastic evolution equations
Gyöngy, I., and Millet, A · 2005
Cited alongside, same era.
Statistical Romberg extrapolation: a new variance reduction method and applications to option pricing
Kebaier, A · 2005
Cited alongside, same era.
On numerical approximation of stochastic Burgers’ equation
Alabert, A., and Gyöngy, I · 2006
Cited alongside, same era.
Ergodicity of the 2D Navier-Stokes equations with degenerate stochastic forcing
Hairer, M., and Mattingly, J. C · 2006
Cited alongside, same era.
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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First order strong approximations of scalar SDEs with values in a domain
Neuenkirch, A., and Szpruch, L · 2012
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Tretyakov, M., and Zhang, Z · 2012
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Galerkin approximations for the stochastic Burgers equation
Blömker, D., and Jentzen, A · 2013
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Full discretization of the stochastic Burgers equation with correlated noise
Blömker, D., Kamrani, M., and Hosseini, S. M · 2013
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Global flows for stochastic differential equations without global Lipschitz conditions
Fang, S., Imkeller, P., and Zhang, T · 2007
Cited alongside, same era.
A concise course on stochastic partial differential equations
Prévôt, C., and Röckner, M · 2007
Cited alongside, same era.
Improved multilevel Monte Carlo convergence using the Milstein scheme
Giles, M. B · 2008
Cited alongside, same era.
Improved moment estimates for invariant measures of semilinear diffusions in Hilbert spaces and applications
Es-Sarhir, A., and Stannat, W · 2010
Cited alongside, same era.
Study of noise-induced transitions in the Lorenz system using the minimum action method
Zhou, X., and E, W · 2010
Cited alongside, same era.
Rates of convergence for discretizations of the stochastic incompressible Navier-Stokes equations
Carelli, E., and Prohl, A · 2011
Cited alongside, same era.
Non-asymptotic mixing of the MALA algorithm
Bou-Rabee, N., and Hairer, M · 2013
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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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Cox, S. G., Hutzenthaler, M., and Jentzen, A · 2013
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Stochastic stability of the Ekman spiral
Hieber, M., and Stannat, W · 2013
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Hutzenthaler, M., Jentzen, A., and Wang, X · 2013
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Convergence of numerical methods for stochastic differential equations in mathematical finance
Kloeden, P. E., and Neuenkirch, A · 2013
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On the backward Euler approximation of the stochastic Allen-Cahn equation
Kovács, M., Larsson, S., and Lindgren, F · 2013
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Strong convergence rates for backward Euler-Maruyama method for non-linear dissipative-type stochastic differential equations with super-linear diffusion coefficients
Mao, X., and Szpruch, L · 2013
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Sabanis, S · 2013
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A note on tamed Euler approximations
Sabanis, S · 2013
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Lattice approximation for stochastic reaction diffusion equations with one-sided Lipschitz condition
Sauer, M., and Stannat, W · 2013
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Szpruch, L · 2013
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Loss of regularity for Kolmogorov equations
Hairer, M., Hutzenthaler, M., and Jentzen, A · 2014
Closest in time.
Hutzenthaler, M., and Jentzen, A · 2014
Closest in time.