Numerical conservation issues for jump Pearson diffusions

DOI10.1016/j.apnum.2023.05.012zbMath1524.65030OpenAlexW4377101720MaRDI QIDQ6169251

Carmela Scalone, Stefano Di Giovacchino

Publication date: 11 July 2023

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2023.05.012

zbMATH Keywords

stabilityPoisson jumpstochastic theta methodslong term behavior

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Cites Work

• Unnamed Item
• Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise
• Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
• Numerical solution of jump-diffusion LIBOR market models
• Theory of stochastic differential equations with jumps and applications.
• Almost sure stability of linear stochastic differential equations with jumps
• Drift-preserving numerical integrators for stochastic Hamiltonian systems
• Filon quadrature for stochastic oscillators driven by time-varying forces
• Positivity preserving stochastic \(\theta\)-methods for selected SDEs
• Closed-form formulas for conditional moments of inhomogeneous Pearson diffusion processes
• Qualitative properties of different numerical methods for the inhomogeneous geometric Brownian motion
• Destabilising nonnormal stochastic differential equations
• Numerical preservation issues in stochastic dynamical systems by \(\vartheta\)-methods
• On the numerical structure preservation of nonlinear damped stochastic oscillators
• Long-term analysis of stochastic \(\theta\)-methods for damped stochastic oscillators
• Computing the closest real normal matrix and normal completion
• Construction of positivity preserving numerical method for jump-diffusion option pricing models
• Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise
• Numerical methods for nonlinear stochastic differential equations with jumps
• Mean-square contractivity of stochastic \(\vartheta\)-methods
• A cumulant approach for the first-passage-time problem of the Feller square-root process
• Long Time Accuracy of Lie--Trotter Splitting Methods for Langevin Dynamics
• STOCHASTIC STABILIZATION OF DYNAMICAL SYSTEMS USING LÉVY NOISE
• Series Expansions for the First Passage Distribution of Wong–Pearson Jump-Diffusions
• Asymptotic Stability of Stochastic Differential Equations Driven by Lévy Noise
• Asymptotic Stability of a Jump-Diffusion Equation and Its Numerical Approximation
• Mean-Square and Asymptotic Stability of the Stochastic Theta Method
• Numerical Methods for Stochastic Systems Preserving Symplectic Structure
• Financial Modelling with Jump Processes
• Lévy Processes and Stochastic Calculus
• Drift-preserving numerical integrators for stochastic Poisson systems
• First and second moment reversion for a discretized square root process with jumps
• The Pearson Diffusions: A Class of Statistically Tractable Diffusion Processes
• Option pricing when underlying stock returns are discontinuous
• Long-Term Analysis of Stochastic Hamiltonian Systems Under Time Discretizations
• Numerical conservation issues for the stochastic Korteweg-de Vries equation
• A long term analysis of stochastic theta methods for mean reverting linear process with jumps

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