A stochastic calculus for continuous N-parameter strong martingales
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.
Year of publication: |
1985
|
---|---|
Authors: | Imkeller, Peter |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 20.1985, 1, p. 1-40
|
Publisher: |
Elsevier |
Keywords: | N-parameter strong martingales Ito-type formulas Burkholder's inequalities |
Saved in:
Online Resource
Saved in favorites
Similar items by person
-
Optimal stopping with f-expectations: The irregular case
Grigorova, Miryana, (2017)
-
Doubly reflected BSDEs and epsilon f-Dynkin games: Beyond the right-continuous case
Grigorova, Miryana, (2018)
-
A two state model for noise-induced resonance in bistable systems with delay
Fischer, Markus, (2005)
- More ...