Almost sure exponential stability of the \(\theta\)-method for stochastic differential equations

DOI10.1016/j.spl.2012.05.004zbMath1250.60030OpenAlexW2077083259MaRDI QIDQ452876

Lin Chen, Fuke Wu

Publication date: 18 September 2012

Published in: Statistics \& Probability Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.spl.2012.05.004

zbMATH Keywords

stochastic differential equationsalmost sure exponential stabilitysemimartingale convergence theorem\(\theta \)-methodone-sided linear growth

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stochastic stability in control theory (93E15) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items

Asymptotic moment boundedness of the stochastic theta method and its application for stochastic differential equations, Asymptotic exponential stability of modified truncated EM method for neutral stochastic differential delay equations, The stochastic \(\theta\) method for stationary distribution of stochastic differential equations with Markovian switching, Stationary distribution of the stochastic theta method for nonlinear stochastic differential equations, \(p\)th moment \((p \in (0, 1))\) and almost sure exponential stability of the exact solutions and modified truncated EM method for stochastic differential equations, Almost sure stability of stochastic theta methods with random variable stepsize for stochastic differential equations, Exponential mean-square stability of the improved split-step theta methods for non-autonomous stochastic differential equations, Exponential mean-square stability of the θ-method for neutral stochastic delay differential equations with jumps, Convergence and almost sure exponential stability of implicit numerical methods for a class of highly nonlinear neutral stochastic differential equations with constant delay, Choice of \({\theta}\) and mean-square exponential stability in the stochastic theta method of stochastic differential equations, Exponential stability of the exact solutions and \(\theta\)-EM approximations to neutral SDDEs with Markov switching

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