On the poisson equation and diffusion approximation 3

By 'Etienne Pardoux, Alexander Yur'evich Veretennikov. 2001

379 citations recorded by the source corpus.

Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of an invariant diffusion density with respect to a parameter. The second establishes a similar smoothness of the solution of the Poisson equation in Rd. The third one states a diffusion approximation result, or in other words an averaging of singularly perturbed diffusion for "fully coupled SDE systems'' or "SDE systems with complete dependence.''

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/bc155edccc4398608e74b5781d598bc74f4903bf

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Citations in the corpus

Examples of moderate deviation principle for diffusion processes (2005, methodology): “admissible, Theorem 2 from Pardoux and Veretennikov, [ 21 ], is no longer applicable.”
Penalized nonparametric mean square estimation of the coefficients of diffusion processes (2007, background): “Moreover, it follows from Proposition 1 in Pardoux and Veretennikov (2001) that there exist constants K > 0, ν > 0 and θ > 0 such that: where β X ( t ) denotes the β -mixing coeﬃcient of ( X t ) and is given by The norm k .”
On large deviations of coupled diffusions with time scale separation (2013, methodology): “13) when c(·),m(·)φ is a gradient; see Pardoux and Veretennikov [35].”
Subgeometric rates of convergence of f-ergodic strong Markov processes (2006, neutral): “∗CMAP, Ecole Polytechnique, 91128 Palaiseau Cedex, France. douc@cmapx.polytechnique.fr †CNRS/LTCI, 46 rue Barrault, 75634 Paris Cedex 13, France. gfort@tsi.enst.fr ‡Ceremade, Université Paris Dauphine, Place Marechal de Lattre de Tassigny, 75775 Paris cedex 16, France. guillin@ceremade.dauphine.fr”
Characterizations of Overtaking Optimality for Controlled Diffusion Processes (2008, neutral): “the proof of Theorem 2.12 of Hashemi and Heunis [18]. (Related results appear in [15] and [ 32 ].)”
Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, background): “where Y = {Y (t), t ≥ 0} is a diffusion process with generator GY [48].”
Diffusion models and steady-state approximations for exponentially ergodic Markovian queues. (2014, background): “This follows exactly as in part (c) of [21], Theorem 1, using (23).”
Diffusion approximation for fully coupled stochastic differential equations (2020, methodology): “Later on, the results of [42, 43, 44] for the Poisson equation (1.”