 A stochastic calculus for continuous N-parameter strong martingalesPeter Imkeller Stochastic Processes and their Applications, 1985, vol. 20, issue 1, 1-40 Abstract: Let M be a 4N-integrable, real-valued continuous N-parameter strong martingale. Burkholder's inequalities prove to be an adequate tool to control the quadratic oscillations of M and the integral processes associated with it (i.e. multiple 1-stochastic integrals with respect to M and its quadratic variation) such that a 1-stochastic calculus for M can be designed. As the main results of this calculus, several Ito-type formulas are established: one in terms of the integral processes associated with M, another one in terms of the so-called 'variations', i.e. stochastic measures which arise as the limits of straightforward and simple approximations by Taylor's formula; finally, a third one which is derived from the first by iterated application of a stochastic version of Green's formula and which may be the strong martingale form of a prototype for general martingales. Keywords: N-parameter; strong; martingales; Ito-type; formulas; Burkholder's; inequalities (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:20:y:1985:i:1:p:1-40 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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