The modulus of continuity of a stochastic process is a random element for any fixed mesh size. We provide upper bounds for the moments of the modulus of continuity of Ito processes with possibly unbounded coefficients, starting from the special case of Brownian motion. References to known results for the case of Brownian motion and Ito processes with uniformly bounded coefficients are included. As an application, we obtain the rate of strong convergence of Euler-Maruyama schemes for the approximation of stochastic delay differential equations satisfying a Lipschitz condition in supremum norm.
On the moments of the modulus of continuity of Ito processes / Nappo, Giovanna; Fischer, Markus. - In: STOCHASTIC ANALYSIS AND APPLICATIONS. - ISSN 0736-2994. - STAMPA. - 28:(2010), pp. 103-122. [10.1080/07362990903415825]
On the moments of the modulus of continuity of Ito processes
NAPPO, Giovanna;
2010
Abstract
The modulus of continuity of a stochastic process is a random element for any fixed mesh size. We provide upper bounds for the moments of the modulus of continuity of Ito processes with possibly unbounded coefficients, starting from the special case of Brownian motion. References to known results for the case of Brownian motion and Ito processes with uniformly bounded coefficients are included. As an application, we obtain the rate of strong convergence of Euler-Maruyama schemes for the approximation of stochastic delay differential equations satisfying a Lipschitz condition in supremum norm.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
