The paper surveys the basic ideas of stochastic calculus via regu- larizations 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 / A. Cosso, C. Di Girolami, F. Russo (CONTEMPORARY MATHEMATICS). - In: Probability on Algebraic and Geometric Structures / [a cura di] G. Budzban, H.R. Hughes, H. Schurz. - [s.l] : American Mathematical Society, 2016. - ISBN 978-1-4704-1945-5. - pp. 43-65 (( convegno Probability on Algebraic and Geometric Structures tenutosi a Carbondale nel 2014 [10.1090/conm/668/13396].

Calculus via regularizations in Banach spaces and Kolmogorov-type path-dependent equations

A. Cosso;
2016

Abstract

The paper surveys the basic ideas of stochastic calculus via regu- larizations 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.
Stochastic calculus via regularization in Banach spaces; path dependent Komogorov equation; functional Itˆo calculus
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/931985
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