Hypoellipticity theorems and conditional laws

Chaleyat-Maurel, Mireille; Michelet, Dominique

doi:10.1007/bf00531840

Cited by 33 publications

(26 citation statements)

References 18 publications

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“…One of the object of [14] or [17] was to use Malliavin's calculus for time dependent systems in order to get smoothness of conditional laws as the ones which appear in filtering theory. Our results give the correct hypothesis for section 2 of [17].…”

Section: Filteringmentioning

confidence: 99%

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Hypoelliptic non-homogeneous diffusions

Cattiaux

Mesnager

2002

Probab Theory Relat Fields

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be a time dependent second order operator, written in usual or Hörmander form. We study the regularity of the law of the associated non-homogeneous (time dependent) diffusion process, under Hörmander's like conditions. Coefficients are only Hölder continuous in time. The main tool is Malliavin calculus. Our results extend and correct previous ones ([17] and related works, [15]). Related topics like filtering theory, killed or reflected processes, parabolic hypoellipticity are also discussed.

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Section: Filteringmentioning

confidence: 99%

“…We shall now study parabolic-hypoellipticity as discussed in [11], [14] or [22], that is the regularity of solutions of ∂u ∂t where x ts is the solution of (1.1) which starts at x at time t.…”

mentioning

confidence: 99%

Hypoelliptic non-homogeneous diffusions

Cattiaux

Mesnager

2002

Probab Theory Relat Fields

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“…Comme dans [4], on introduit, pour a dans R, le potentiel de Bessel A, qui agit sur S' (IW7 (espace des distributions temperees) par la formule suivante: …”

Section: I I Espaces De Sobolevunclassified

Un théorème d'unicité pour l'equation de zakaï

Chaleyat-Maurel¹,

Michelet

Pardoux³

1990

Stochastics and Stochastic Reports

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“…Clark [9] and Davis [11]. Fortunatedly the time dependent gauge transformation 2) gives dp = exp(-°"2,h;y;)c exp(°"2,h;y;)P and to use the version of the Baker-Campbell-Hausdorff formula which says 2) effectively to calculate certain desired conditional expectations.…”

Section: Robustness and Numerical Mattersmentioning

confidence: 99%

Lie Algebraic Method in Filtering and Identification

Hazewinkel¹

1988

Stochastic Processes in Physics and Engineering

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ABSTRACT. These lectures concern (nonlinear) filtering. Very roughly the art of obtaining best estimates for some stochastic time-varying variable x on the basis of observations of another process y. The more concrete object under consideration being a stochastic dynamical system dx=f(x)dt+G(x)dw, where w is Wiener noise, with observations dy=h(x)dt+dv, corrupted by further noise. The subject as presented here involves ideas and techniques from Lie algebra theory, stochastics, differential topology, approximation theory and partial differential equations and has relations with quantum theory and stochastic physics. The lectures are adressed to practitioners in any one of these areas assuming that as a rule they are not experts in the other ones.

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Hypoellipticity theorems and conditional laws

Cited by 33 publications

References 18 publications

Hypoelliptic non-homogeneous diffusions

Hypoelliptic non-homogeneous diffusions

Un théorème d'unicité pour l'equation de zakaï

Lie Algebraic Method in Filtering and Identification

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