Optimal sampling design for global approximation of jump diffusion stochastic differential equations

DOI10.1080/17442508.2018.1521810zbMath1500.60033arXiv1701.08311OpenAlexW2891854843WikidataQ129216543 ScholiaQ129216543MaRDI QIDQ5086424

Paweł Przybyłowicz

Publication date: 5 July 2022

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.08311

zbMATH Keywords

Wiener processnonhomogeneous Poisson processasymptotically optimal algorithmminimal strong errorstandard informationjump commutativity condition

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Jump processes on general state spaces (60J76)

Related Items

Efficient Approximation of SDEs Driven by Countably Dimensional Wiener Process and Poisson Random Measure, Milstein scheme for stochastic differential equation with Markovian switching and Lévy noise, Strong Convergence of Jump-Adapted Implicit Milstein Method for a Class of Nonlinear Jump-Diffusion Problems, Existence, uniqueness, and approximation of solutions of jump-diffusion SDEs with discontinuous drift

Cites Work

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• Optimal global approximation of stochastic differential equations with additive Poisson noise
• Optimal approximation of stochastic integrals with respect to a homogeneous Poisson process
• On tamed Milstein schemes of SDEs driven by Lévy noise
• A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations
• Optimal global approximation of SDEs with time-irregular coefficients in asymptotic setting
• The theory of stochastic processes. III.
• Strong convergence rates for backward Euler on a class of nonlinear jump-diffusion problems
• Strong approximations of stochastic differential equations with jumps
• Numerical solution of stochastic differential equations with jumps in finance
• Higher-order implicit strong numerical schemes for stochastic differential equations
• Optimal global approximation of jump-diffusion SDEs via path-independent step-size control
• Theory of stochastic differential equations with jumps and applications.
• Minimal asymptotic error for one-point approximation of SDEs with time-irregular coefficients
• Stochastic simulation and Monte Carlo methods. Mathematical foundations of stochastic simulation
• Strong approximation of solutions of stochastic differential equations with time-irregular coefficients via randomized Euler algorithm
• Numerical methods for nonlinear stochastic differential equations with jumps
• Optimal approximation of SDE's with additive fractional noise
• The Order of Approximations for Solutions of Itô-Type Stochastic Differential Equations with Jumps
• The optimal discretization of stochastic differential equations
• Nonlinear Lebesgue and Itô integration problems of high complexity