A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.
A note on symmetries of diffusions within a martingale problem approach / F.C. DE VECCHI, P. Morando, S. Ugolini. - In: STOCHASTICS AND DYNAMICS. - ISSN 0219-4937. - 19:2(2019). [10.1142/S0219493719500114]
A note on symmetries of diffusions within a martingale problem approach
F.C. DE VECCHI;P. Morando;S. Ugolini
2019
Abstract
A geometric reformulation of the martingale problem associated with a set of diffusion processes is proposed. This formulation, based on second-order geometry and Itô integration on manifolds, allows us to give a natural and effective definition of Lie symmetries for diffusion processes.
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