| Omari Purtukhia, Valeriane Jokhadze, Ekaterine Namgalauri Martingale Representation and the Problem of Nonlinear Filtration |
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| Abstract. We study Brownian functionals, the conditional mathematical expectation of which with respect to natural filtration (the so-called filter) is not stochastically smooth from the point of view of their representability as a stochastic Itô integral with an explicit form of the integrand. The considered class of functionals also includes those that are not smooth in the sense of Malliavin, to which both the well-known Clark-Ocone formula (1984) and its generalization, the Glonti-Purtukhia representation (2017), are inapplicable. |
| Keywords: Malliavin (stochastic) derivative, martingale representation, filtering problem, Clark-Ocone formula, Glonti-Purtukhia representation |
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| DOI: https://doi.org/10.54381/pci2023.07 |
