Strong approximation of stochastic processes at random times and application to their exact simulation

DOI10.1080/17442508.2016.1267179zbMath1394.60062OpenAlexW2612515786MaRDI QIDQ4584675

Mohamed Mrad, Emmanuel Gobet

Publication date: 4 September 2018

Published in: Stochastics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17442508.2016.1267179

zbMATH Keywords

fractional Brownian motionlocal timestrong approximationexact simulationiterated Brownian motionEuler schemes

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Stopping times; optimal stopping problems; gambling theory (60G40) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35)

Related Items

Solving some stochastic partial differential equations driven by Lévy noise using two SDEs*, Convergence rate of strong approximations of compound random maps, application to SPDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• First time to exit of a continuous Itô process: general moment estimates and \({\mathbf{L}}_{1}\)-convergence rate for discrete time approximations
• Unbiased simulation of stochastic differential equations using parametrix expansions
• The Skorokhod embedding problem and its offspring
• Probabilistic construction of the solution of some higher order parabolic differential equation
• Brownian motion in a Brownian crack
• Exact rates of convergence to Brownian local time
• Brownian-time processes: The PDE connection and the half-derivative generator
• Strong approximation of fractional Brownian motion by moving averages of simple random walks.
• Discretization error in simulation of one-dimensional reflecting Brownian motion
• Fractional fields and applications
• Iterating Brownian motions, ad libitum
• A note on the sharp \(L^p\)-convergence rate of upcrossings to the Brownian local time
• An Itô type formula for the fractional Brownian motion in Brownian time
• Long memory in continuous-time stochastic volatility models
• Brownian-time processes: The PDE connection II and the corresponding Feynman-Kac formula
• Multilevel Monte Carlo Path Simulation
• Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$
• A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm
• Fractional Brownian Motions, Fractional Noises and Applications