Almost sure instability of the equilibrium solution of a Milstein-type stochastic difference equation

DOI10.1016/j.camwa.2013.06.020zbMath1350.39011OpenAlexW2090684509MaRDI QIDQ316375

Peter Palmer, Cónall Kelly, Aleksandra Rodkina

Publication date: 27 September 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2013.06.020

zbMATH Keywords

Itô stochastic differential equationmultiplicative noisemartingale convergencea.s. instabilitydiscrete Itô formulaEuler-Milstein discretisationstochastic difference equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Discrete version of topics in analysis (39A12) Stability theory for difference equations (39A30) Stochastic difference equations (39A50)

Related Items (3)

Adaptive timestepping for pathwise stability and positivity of strongly discretised nonlinear stochastic differential equations ⋮ Instability and stability of solutions of systems of nonlinear stochastic difference equations with diagonal noise ⋮ Global stabilization and destabilization by the state dependent noise with particular distributions

Cites Work

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• Application of a discrete Itô formula to determine stability (instability) of the equilibrium of a scalar linear stochastic difference equation
• A comparative linear mean-square stability analysis of Maruyama- and Milstein-type methods
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Almost sure exponential stability of neutral stochastic differential difference equations
• Non-exponential stability and decay rates in nonlinear stochastic difference equations with unbounded noise
• Probability with Martingales
• Almost sure asymptotic stability analysis of the θ-Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

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