Sticky Brownian Motion and Its Numerical Solution

DOI10.1137/19M1268446zbMath1444.60048arXiv1906.06803OpenAlexW3006462988MaRDI QIDQ5216248

Nawaf Bou-Rabee, Miranda C. Holmes-Cerfon

Publication date: 17 February 2020

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.06803

zbMATH Keywords

Fokker-Planck equationfinite difference methodsKolmogorov equationMarkov jump processsticky Brownian motionMarkov chain approximation methodFeller boundary conditionsticky random walkgeneralized Wentzell boundary condition

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Initial-boundary value problems for second-order parabolic equations (35K20) Brownian motion (60J65) Heat equation (35K05) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Diffusion processes (60J60) Numerical solutions to stochastic differential and integral equations (65C30)

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Cites Work

• A structure-preserving numerical discretization of reversible diffusions
• A probabilistic solution to the Stroock-Williams equation
• Steady states in a structured epidemic model with Wentzell boundary condition
• Probability methods for the convergence of finite difference approximations to partial differential equations
• Generalized second order differential operators and their lateral conditions
• Probability methods for approximations in stochastic control and for elliptic equations
• Stochastic methods. A handbook for the natural and social sciences
• Large deviations techniques and applications.
• Association rates of diffusion-controlled reactions in two dimensions
• Sticky Brownian motion as the strong limit of a sequence of random walks
• The approximate calculation of invariant measures of diffusions via finite difference approximations to degenerate elliptic partial differential equations
• Probabilistic methods for finite difference approximations to degenerate elliptic and parabolic equations with Neumann and Dirichlet boundary conditions
• Finite difference methods for the weak solutions of the Kolmogorov equation for the density of both diffusion and conditional diffusion processes
• A survey of results on nonlinear Venttsel problems.
• The heat equation with generalized Wentzell boundary condition.
• Fick law and sticky Brownian motions
• Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection
• Multiple scale and singular perturbation methods
• Large deviations for sticky Brownian motions
• A robust numerical algorithm for studying biomolecular transport processes
• Sticky couplings of multidimensional diffusions with different drifts
• Probability limit theorems and the convergence of finite difference approximations of partial differential equations
• Brownian motions on a half line
• The parabolic differential equations and the associated semigroups of transformation
• An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations
• Stochastic differential equations for sticky Brownian motion
• Langevin dynamics with constraints and computation of free energy differences
• Colloidal matter: Packing, geometry, and entropy
• Numerical methods for controls for nonlinear stochastic systems with delays and jumps: applications to admission control
• Transition Path Theory for Markov Jump Processes
• Numerical approximations for stochastic systems with delays in the state and control
• Sticky Brownian motion as the limit of storage processes
• Linear second order elliptic equations with Venttsel boundary conditions
• Linear parabolic equations with venttsel initial boundary conditions
• Rates of Convergence for Approximation Schemes in Optimal Control
• Euler schemes and half-space approximation for the simulation of diffusion in a domain
• Monte Carlo on Manifolds: Sampling Densities and Integrating Functions
• SPECTRWM: Spectral Random Walk Method for the Numerical Solution of Stochastic Partial Differential Equations
• Numerical Approximations for Stochastic Differential Games: The Ergodic Case
• A symmetrized Euler scheme for an efficient approximation of reflected diffusions
• Numerical Approximations for Stochastic Differential Games
• $C_0$-semigroups generated by second order differential operators with general Wentzell boundary conditions
• Numerical computation of rare events via large deviation theory
• A positive interest rate model with sticky barrier
• Continuous-time Random Walks for the Numerical Solution of Stochastic Differential Equations
• Projection of diffusions on submanifolds: Application to mean force computation
• Diffusion processes with boundary conditions
• Diffusion Processes in One Dimension
• Markoff Chains--Denumerable Case
• Topics in the Theory of Markoff Chains
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