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

Abstract

We study the convergence rates of strong approximations of stochastic processes (possibly non semi-martingales) at random times (possibly non stopping times). Examples include Brownian local times at random points, Fractional Brownian motions or diffusion processes at Brownian time. These strong approximation results allow to design an exact simulation scheme.

Keywords:

• Strong approximation
• Euler schemes
• iterated Brownian motion
• local time
• Fractional Brownian motion
• exact simulation

AMS Subject Classifications:

• 60Hxx
• 60Gxx

Notes

No potential conflict of interest was reported by the authors.

1 To be precise, their scheme converges towards some fBM and not necessarily .

Additional information

Funding

This work was supported by the Chaire Risques Financiers of the Risk Foundation; the Finance for Energy Market Research Centre.