Stability and error analysis of an implicit Milstein finite difference scheme for a two-dimensional Zakai SPDE

DOI10.1007/s10543-019-00761-8zbMath1437.65006arXiv1802.07682OpenAlexW2964081646WikidataQ127659427 ScholiaQ127659427MaRDI QIDQ2009114

Zhen-Ru Wang, Christoph Reisinger

Publication date: 27 November 2019

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.07682

zbMATH Keywords

stochastic partial differential equationsmean-square stabilityMilstein schemesplitting schemes\(L_2\)-convergencestochastic finite differences

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Numerical methods for discrete and fast Fourier transforms (65T50) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (3)

A derivative-free Milstein type approximation method for SPDEs covering the non-commutative noise case ⋮ Numerical simulations of nonlinear stochastic Newell-Whitehead-Segel equation and its measurable properties ⋮ Analysis of sparse grid multilevel estimators for multi-dimensional Zakai equations

Cites Work

• Unnamed Item
• Finite difference schemes for linear stochastic integro-differential equations
• The numerical approximation of stochastic partial differential equations
• Stiffness of ODEs
• Convergence of the modified Craig-Sneyd scheme for two-dimensional convection-diffusion equations with mixed derivative term
• Fundamentals of stochastic filtering
• Taylor expansions of solutions of stochastic partial differential equations with additive noise
• An alternating-direction implicit scheme for parabolic equations with mixed derivatives
• Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. I
• Lattice approximations for stochastic quasi-linear parabolic partial differential equations driven by space-time white noise. II
• Implicit scheme for stochastic parabolic partial differential equations driven by space-time white noise
• Exact rates of convergence for a branching particle approximation to the solution of the Zakai equation
• Particle representations for a class of nonlinear SPDEs
• Mean-square stability analysis of approximations of stochastic differential equations in infinite dimensions
• Finite element methods for parabolic stochastic PDE's
• The optimal uniform approximation of systems of stochastic differential equations
• Joint characteristic function and simultaneous simulation of iterated Itô integrals for multiple independent Brownian motions
• Milstein approximation for advection-diffusion equations driven by multiplicative noncontinuous martingale noises
• Multilevel Monte Carlo method for parabolic stochastic partial differential equations
• \(L^p\) and almost sure convergence of a Milstein scheme for stochastic partial differential equations
• A particle approximation of the solution of the Kushner-Stratonovitch equation
• Efficient almost-exact Lévy area sampling
• Towards a Systematic Linear Stability Analysis of Numerical Methods for Systems of Stochastic Differential Equations
• The Numerical Solution of Parabolic and Elliptic Differential Equations
• Sharp error estimates for discretizations of the 1D convection–diffusion equation with Dirac initial data
• Approximate McKean–Vlasov representations for a class of SPDEs
• The approximation of multiple stochastic integrals
• Random Generation of Stochastic Area Integrals
• Convergence of numerical schemes for the solution of parabolic stochastic partial differential equations
• Stochastic Evolution Equations for Large Portfolios of Stochastic Volatility Models
• Analysis of Multi-Index Monte Carlo Estimators for a Zakai SPDE
• Stochastic Finite Differences and Multilevel Monte Carlo for a Class of SPDEs in Finance
• Mean-square stability and error analysis of implicit time-stepping schemes for linear parabolic SPDEs with multiplicative Wiener noise in the first derivative
• Stochastic Evolution Equations in Portfolio Credit Modelling
• Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
• Discretization and Simulation of the Zakai Equation
• Stochastic evolution equations

This page was built for publication: Stability and error analysis of an implicit Milstein finite difference scheme for a two-dimensional Zakai SPDE