Set-indexed stochastic analysis and set-indexed stochastic calculus are faced here with a new approach of dimension’s reduction. We introduce a new tool (main flow) in order to deal with one-parameter calculus in set-indexed framework. We prove an Itô formula for any Brownian functional where the Brownian component is not a martingale on the whole set of indices but induces such a martingale. As first extensions, we provide definitions of bracket and local time in set-indexed context.
Set-Indexed Itô Calculus Along Paths / G. Aletti, D. Saada. - In: STOCHASTIC ANALYSIS AND APPLICATIONS. - ISSN 0736-2994. - 22:4(2004), pp. 1027-1066. [10.1081/SAP-120037630]
Set-Indexed Itô Calculus Along Paths
G. AlettiPrimo
;
2004
Abstract
Set-indexed stochastic analysis and set-indexed stochastic calculus are faced here with a new approach of dimension’s reduction. We introduce a new tool (main flow) in order to deal with one-parameter calculus in set-indexed framework. We prove an Itô formula for any Brownian functional where the Brownian component is not a martingale on the whole set of indices but induces such a martingale. As first extensions, we provide definitions of bracket and local time in set-indexed context.
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