Weak Convergence of Finite Element Approximations of Linear Stochastic Evolution Equations with Additive Lévy Noise

SIAM/ASA Journal on Uncertainty Quantification ◽

10.1137/15m1009792 ◽

2015 ◽

Vol 3 (1) ◽

pp. 1159-1199 ◽

Author(s):

Mihály Kovács ◽

Felix Lindner ◽

René L. Schilling

Keyword(s):

Finite Element ◽

Weak Convergence ◽

Evolution Equations ◽

Lévy Noise ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Finite Element Approximations ◽

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Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

BIT Numerical Mathematics ◽

10.1007/s10543-012-0405-1 ◽

2012 ◽

Author(s):

Mihály Kovács ◽

Stig Larsson ◽

Fredrik Lindgren

Keyword(s):

Finite Element ◽

Weak Convergence ◽

Additive Noise ◽

Evolution Equations ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Fully Discrete ◽

Finite Element Approximations

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Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise

BIT Numerical Mathematics ◽

10.1007/s10543-011-0344-2 ◽

2011 ◽

Vol 52 (1) ◽

pp. 85-108 ◽

Author(s):

Mihály Kovács ◽

Stig Larsson ◽

Fredrik Lindgren

Keyword(s):

Finite Element ◽

Weak Convergence ◽

Additive Noise ◽

Evolution Equations ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Finite Element Approximations

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Pathwise uniqueness for stochastic evolution equations with Hölder drift and stable Lévy noise

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-018-0511-0 ◽

2018 ◽

Vol 25 (3) ◽

Author(s):

Desheng Yang

Keyword(s):

Evolution Equations ◽

Lévy Noise ◽

Pathwise Uniqueness ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

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Hyperbolic Type Stochastic Evolution Equations with Lévy Noise

Acta Applicandae Mathematicae ◽

10.1007/s10440-012-9787-y ◽

2012 ◽

Vol 125 (1) ◽

pp. 193-208 ◽

Author(s):

Hongbo Fu ◽

Jicheng Liu ◽

Li Wan

Keyword(s):

Evolution Equations ◽

Hyperbolic Type ◽

Lévy Noise ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

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A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations

Mathematics of Computation ◽

10.1090/mcom/3421 ◽

2019 ◽

Vol 88 (320) ◽

pp. 2793-2825

Author(s):

Raphael Kruse ◽

Yue Wu

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Evolution Equations ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Galerkin Finite Element Method ◽

Galerkin Finite Element ◽

Fully Discrete ◽

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Weak Convergence of Probability Measures of Trotter–Kato Approximate Solutions of Stochastic Evolution Equations

Infosys Science Foundation Series - Applied Probability and Stochastic Processes ◽

10.1007/978-981-15-5951-8_26 ◽

2020 ◽

pp. 441-456

Author(s):

T. E. Govindan

Keyword(s):

Weak Convergence ◽

Evolution Equations ◽

Approximate Solutions ◽

Probability Measures ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Convergence Of Probability Measures

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Weak convergence of solutions of stochastic evolution equations on nuclear spaces

Stochastic Partial Differential Equations and Applications II - Lecture Notes in Mathematics ◽

10.1007/bfb0083940 ◽

1989 ◽

pp. 119-131 ◽

Author(s):

G. Kallianpur ◽

V. Pérez-Abreu

Keyword(s):

Weak Convergence ◽

Evolution Equations ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Convergence Of Solutions ◽

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Weak convergence rates for stochastic evolution equations and applications to nonlinear stochastic wave, HJMM, stochastic Schrödinger and linearized stochastic Korteweg–de Vries equations

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/s00033-018-1060-4 ◽

2018 ◽

Vol 70 (1) ◽

Author(s):

Philipp Harms ◽

Marvin S. Müller

Keyword(s):

Weak Convergence ◽

Evolution Equations ◽

Convergence Rates ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

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Weak Convergence Rates for Euler-Type Approximations of Semilinear Stochastic Evolution Equations with Nonlinear Diffusion Coefficients

Foundations of Computational Mathematics ◽

10.1007/s10208-020-09448-x ◽

2020 ◽

Author(s):

Arnulf Jentzen ◽

Ryan Kurniawan

Keyword(s):

Weak Convergence ◽

Diffusion Coefficients ◽

Nonlinear Diffusion ◽

Evolution Equations ◽

Convergence Rates ◽

Stochastic Evolution ◽

Stochastic Evolution Equations

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Smoothness of solutions of stochastic evolution equations and the existence of a filtering transition density

Nagoya Mathematical Journal ◽

10.1017/s0027763000019619 ◽

1981 ◽

Vol 84 ◽

pp. 195-208 ◽

Author(s):

B. L. Rozovskii ◽

A. Shimizu

Keyword(s):

Evolution Equations ◽

Transition Density ◽

Stochastic Evolution ◽

Stochastic Evolution Equations ◽

Smoothness Of Solutions

In this paper, we shall discuss the smoothness of solutions of stochastic evolution equations, which has been investigated in N. V. Krylov and B. L. Rozovskii [2] [3], to establish the existence of a filtering transition density.

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