A strong and weak approximation scheme for stochastic differential equations driven by a time-changed Brownian motion

• Autorzy: Jum E. , Kobayashi K.
• Języki publikacji: EN

Abstrakty

EN

This paper establishes a discretization scheme for a large class of stochastic differential equations driven by a time-changed Brownian motion with drift, where the time change is given by a general inverse subordinator. The scheme involves two types of errors: one generated by application of the Euler-Maruyama scheme and the other ascribed to simulation of the inverse subordinator. With the two errors carefully examined, the orders of strong and weak convergence are established. In particular, an improved error estimate for the Euler-Maruyama scheme is derived, which is required to guarantee the strong convergence. Numerical examples are attached to support the convergence results.

Słowa kluczowe

EN

stochastic differential equation; numerical approximation; order of convergence; time-changed Brownian motion; inverse subordinator

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2016
• Tom: Vol. 36, Fasc. 2
• Strony: 201--220
• Opis fizyczny: Bibliogr. 29 poz., wykr.

Twórcy

autor

Jum E.

• Winston-Salem, NC, USA

autor

Kobayashi K.

• Fordham University, 113 West 60th Street, Room 813, New York, NY 10023, USA

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).