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EnglishThe paper surveys the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with windows of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution.
Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations / Cosso, Andrea; Di Girolami, Cristina; Russo, Francesco. - STAMPA. - 668(2016), pp. 43-65.
| Titolo: | Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations |
| Autore/i: | Cosso, Andrea; Di Girolami, Cristina; Russo, Francesco |
| Autore/i Unibo: | |
| Anno: | 2016 |
| Titolo del libro: | PROBABILITY ON ALGEBRAIC AND GEOMETRIC STRUCTURES |
| Pagina iniziale: | 43 |
| Pagina finale: | 65 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1090/conm/668/1.3396 |
| Abstract: | The paper surveys the basic ideas of stochastic calculus via regularizations in Banach spaces and its applications to the study of strict solutions of Kolmogorov path dependent equations associated with windows of diffusion processes. One makes the link between the Banach space approach and the so called functional stochastic calculus. When no strict solutions are available one describes the notion of strong-viscosity solution which alternative (in infinite dimension) to the classical notion of viscosity solution. |
| Data stato definitivo: | 16-nov-2017 |
| Appare nelle tipologie: | 2.01 Capitolo / saggio in libro |
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