On the Moments of the Modulus of Continuity of Itô Processes

DOI10.1080/07362990903415825zbMath1182.60021OpenAlexW2000706650MaRDI QIDQ3405554

Markus Fischer, Giovanna Nappo

Publication date: 10 February 2010

Published in: Stochastic Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/07362990903415825

zbMATH Keywords

modulus of continuitystochastic delay differential equationsItô processesstrong convergence of Euler-Maruyama schemes

Mathematics Subject Classification ID

Extreme value theory; extremal stochastic processes (60G70) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Brownian motion (60J65) Diffusion processes (60J60) Sample path properties (60G17) Stochastic functional-differential equations (34K50) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

Strong approximation of stochastic differential equations driven by a time-changed Brownian motion with time-space-dependent coefficients, On the pathwise approximation of stochastic differential equations, Strong Convergence Rates for Euler Approximations to a Class of Stochastic Path-Dependent Volatility Models, Hydrodynamic limit and propagation of chaos for Brownian particles reflecting from a Newtonian barrier, Tamed-adaptive Euler-Maruyama approximation for SDEs with locally Lipschitz continuous drift and locally Hölder continuous diffusion coefficients, Strong convergence rate for multivalued stochastic differential equations via stochastic theta method, Stein's method for multivariate Brownian approximations of sums under dependence, A class of dimension-free metrics for the convergence of empirical measures, Convergence of a time-stepping scheme to the free boundary in the supercooled Stefan problem, Asymptotic F test in regressions with observations collected at high frequency over long span, Multilevel Monte Carlo simulation for the Heston stochastic volatility model, Time discretization and quantization methods for optimal multiple switching problem, Nonparametric volatility estimation in scalar diffusions: optimality across observation frequencies, Optimally thresholded realized power variations for Lévy jump diffusion models, Statistical convergence of Markov experiments to diffusion limits, On the form of the large deviation rate function for the empirical measures of weakly interacting systems, Convergence of an Euler Scheme for a Hybrid Stochastic-Local Volatility Model with Stochastic Rates in Foreign Exchange Markets, Sup-norm convergence rates for Lévy density estimation, Diffusion approximation of multi-class Hawkes processes: Theoretical and numerical analysis, Rate of convergence for the discrete-time approximation of reflected BSDEs arising in switching problems, Functional approximations via Stein's method of exchangeable pairs, Cone points of Brownian motion in arbitrary dimension, Discrete-type approximations for non-Markovian optimal stopping problems: Part I, Stein's method of exchangeable pairs in multivariate functional approximations, A Dual Algorithm for Stochastic Control Problems: Applications to Uncertain Volatility Models and CVA, Strong approximation of time-changed stochastic differential equations involving drifts with random and non-random integrators, Optimal Switching in Finite Horizon under State Constraints, Semi-implicit Milstein approximation scheme for non-colliding particle systems, Occupation density estimation for noisy high-frequency data

Cites Work

• Unnamed Item
• Unnamed Item
• On approximation of solutions of multidimensional SDE's with reflecting boundary conditions
• The optimal uniform approximation of systems of stochastic differential equations
• Discrete-time approximations of stochastic delay equations: the Milstein scheme.
• Step size control for the uniform approximation of systems of stochastic differential equations with additive noise.
• Euler's approximations of solutions of SDEs with reflecting boundary.
• Approximations for stochastic differential equations with reflecting convex boundaries
• Approximations of the Brownian rough path with applications to stochastic analysis
• Regularity of irregularities on a Brownian path
• Approximation and optimization on the Wiener space
• Sur la distribution limite du terme maximum d'une série aléatoire
• Numerical Solutions of Stochastic Functional Differential Equations
• Moment Convergence of Sample Extremes