Hyperfinite stochastic integration for Levy processes with finite-variation jump part

Herzberg F (2010)
BULLETIN DES SCIENCES MATHEMATIQUES 134(4): 423-445.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
This article links the hyperfinite theory of stochastic integration with respect to certain hyperfinite Levy processes with the elementary theory of pathwise stochastic integration with respect to pure-jump Levy processes with finite-variation jump part. Since the hyperfinite Ito integral is also defined pathwise, these results show that hyperfinite stochastic integration provides a pathwise definition of the stochastic integral with respect to Levy jump-diffusions with finite-variation jump part. As an application, we provide a short and direct nonstandard proof of the generalized Ito formula for stochastic differentials of smooth functions of Levy jump-diffusions whose jumps are bounded from below in norm. (C) 2010 Elsevier Masson SAS. All rights reserved.
Stichworte
Levy processes; Nonstandard analysis; Ito; Stochastic integration; formula
Erscheinungsjahr
2010
Zeitschriftentitel
BULLETIN DES SCIENCES MATHEMATIQUES
Band
134
Ausgabe
4
Seite(n)
423-445
ISSN
0007-4497
Page URI
https://pub.uni-bielefeld.de/record/1795329

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Herzberg F. Hyperfinite stochastic integration for Levy processes with finite-variation jump part. BULLETIN DES SCIENCES MATHEMATIQUES. 2010;134(4):423-445.
Herzberg, F. (2010). Hyperfinite stochastic integration for Levy processes with finite-variation jump part. BULLETIN DES SCIENCES MATHEMATIQUES, 134(4), 423-445. doi:10.1016/j.bulsci.2010.02.004
Herzberg, F. (2010). Hyperfinite stochastic integration for Levy processes with finite-variation jump part. BULLETIN DES SCIENCES MATHEMATIQUES 134, 423-445.
Herzberg, F., 2010. Hyperfinite stochastic integration for Levy processes with finite-variation jump part. BULLETIN DES SCIENCES MATHEMATIQUES, 134(4), p 423-445.
F. Herzberg, “Hyperfinite stochastic integration for Levy processes with finite-variation jump part”, BULLETIN DES SCIENCES MATHEMATIQUES, vol. 134, 2010, pp. 423-445.
Herzberg, F.: Hyperfinite stochastic integration for Levy processes with finite-variation jump part. BULLETIN DES SCIENCES MATHEMATIQUES. 134, 423-445 (2010).
Herzberg, Frederik. “Hyperfinite stochastic integration for Levy processes with finite-variation jump part”. BULLETIN DES SCIENCES MATHEMATIQUES 134.4 (2010): 423-445.

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