Titlebook: Geometry and Invariance in Stochastic Dynamics; Verona, Italy, March Stefania Ugolini,Marco Fuhrman,Barbara Rüdiger Conference proceedings

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,Asymptotic Expansion for a Black–Scholes Model with Small Noise Stochastic Jump-Diffusion Interest ar, we consider the case when the small perturbation is due to a general, but small, noise of Lévy type. Moreover, we provide explicit expressions for the involved expansion coefficients as well as accurate estimates on the remainders.

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Stochastic Geodesics,cal path of an energy functional) to diffusion processes on Riemannian manifolds. These stochastic processes are no longer smooth paths but they are still critical points of a regularised stochastic energy functional. We consider stochastic geodesics on compact Riemannian manifolds and also on (poss

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Higher Order Derivatives of Heat Semigroups on Spheres and Riemannian Symmetric Spaces,phere .. The formula demonstrates that for higher order derivatives there can be a spectrum of decay/growth rates, unlike the generic situation for first derivatives which is fundamental for Bakry-Emery theory. The method used is then applied for higher derivatives for spheres, and could be used for

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,Stochastic Geometric Mechanics with?Diffeomorphisms, mechanics and is shown to play a central role in deriving and understanding the generation of fluid circulation via the Kelvin-Noether theorem for ideal fluids with stochastic advection by Lie transport (SALT).

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McKean Feynman-Kac Probabilistic Representations of Non-linear Partial Differential Equations, solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also fro

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Bernstein Processes, Isovectors and Mechanics, problem stated by Schr?dinger in 1931. Those diffusions satisfy two unusual properties. Although typically not time-homogeneous, they are time reversible. Also their infinitesimal coefficients are specific functions of positive solutions of time adjoint parabolic equations. The symmetries of these

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