Timeline for Most probable path for stochastic Hamiltonian systems

9 events

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Mar 9, 2019 at 6:10	history	edited	YCor		edited tags
Jul 5, 2017 at 20:07	comment	added	ofer zeitouni		More specifically, for nice diffusions $x_t$ the OM functional is $\lim _{\epsilon \to 0} P(\\|x-\phi\\|<\epsilon)/P(\\|x\\|<\epsilon)$ where $\\|\cdot\\|$ is carefully chosen. What is $\\| \cdot \\|$ in your question?
Jul 5, 2017 at 20:06	comment	added	ofer zeitouni		My question was about the definition of "most probable", not about the solution (which is the equation you cite). More specifically, are you measuring only the displacement of Y from a path phi or both X and Y? This issue always arises in the non uniformly elliptic case.
Jul 5, 2017 at 15:51	comment	added	megaproba		yes, in the sense of equation (8,5) page 169 of [The Onsager-Machlup Function as Lagrangian for the Most Probable Path of a Diffusion Process, Detlef Dύrr and Alexander Bach, Commun. math. Phys. 60, 153—170 (1978) ].
Jul 4, 2017 at 15:28	comment	added	ofer zeitouni		What is your definition of most probable path? Is it minimizer of Onsager-Machlup functional?
S Jul 4, 2017 at 14:31	history	edited	Davide Giraudo	CC BY-SA 3.0	added reference-request tag
S Jul 4, 2017 at 14:31	history	suggested	user74045		added reference-request tag
Jul 4, 2017 at 14:22	review	Suggested edits
S Jul 4, 2017 at 14:31
Jul 4, 2017 at 13:53	history	asked	megaproba	CC BY-SA 3.0