Stability of Densities for Perturbed Diffusions and Markov Chains
Konakov, Valentin1 ; Kozhina, Anna2 ; Menozzi, Stéphane3
1 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation.
2 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation and RTG 1953, Institute of Applied Mathematics, Heidelberg University, Germany.
3 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation and LaMME, UMR CNRS 8070, Université d’Evry Val d’Essonne, 23 Boulevard de France, 91037 Evry, France.
ESAIM: Probability and Statistics, Tome 21 (2017), pp. 88-112.

We study the sensitivity of the densities of non degenerate diffusion processes and related Markov Chains with respect to a perturbation of the coefficients. Natural applications of these results appear in models with misspecified coefficients or for the investigation of the weak error of the Euler scheme with irregular coefficients.

Reçu le :
Accepté le :
DOI : 10.1051/ps/2016028
Classification : 60H10, 65C30
Mots-clés : Diffusion processes, Markov chains, parametrix, Hölder coefficients, bounded drifts
Konakov, Valentin 1 ; Kozhina, Anna 2 ; Menozzi, Stéphane 3

1 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation.
2 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation and RTG 1953, Institute of Applied Mathematics, Heidelberg University, Germany.
3 Higher School of Economics, Shabolovka 31, Moscow, Russian Federation and LaMME, UMR CNRS 8070, Université d’Evry Val d’Essonne, 23 Boulevard de France, 91037 Evry, France. 
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     title = {Stability of {Densities} for {Perturbed} {Diffusions} and {Markov} {Chains}},
     journal = {ESAIM: Probability and Statistics},
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Konakov, Valentin; Kozhina, Anna; Menozzi, Stéphane. Stability of Densities for Perturbed Diffusions and Markov Chains. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 88-112. doi : 10.1051/ps/2016028. http://archive.numdam.org/articles/10.1051/ps/2016028/

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