Top

Published in:

2014 | OriginalPaper | Chapter

Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel

Author : Jacques Franchi

Published in: Séminaire de Probabilités XLVI

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

A small time asymptotics of the density is established for a simplified (non-Gaussian, strictly hypoelliptic) second chaos process tangent to the Dudley relativistic diffusion.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter On Bochner-Kolmogorov Theorem

next chapter Onsager-Machlup Functional for Uniformly Elliptic Time-Inhomogeneous Diffusion

R. Azencott, Densité des Diffusions en temps petit: Développements Asymptotiques. Sém. Proba. XVIII, Lecture Notes, vol. 1059 (Springer, New York, 1984), pp. 402–498

G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique hors du cut-locus. Ann. sci. É.N.S. Sér. 4, 21(3), 307–331 (1988)

G. Ben Arous, Développement asymptotique du noyau de la chaleur hypoelliptique sur la diagonale. Ann. Inst. Fourier 39(1), 73–99 (1989)CrossRefMathSciNetMATH

I. Bailleul, J. Franchi, Non-explosion criteria for relativistic diffusions. Ann. Probab. 40(5), 2168–2196 (2012)CrossRefMathSciNetMATH

P. Biane, J. Pitman, M. Yor, Probability laws related to the Jacobi theta and Riemann zeta functions, and Brownian excursions. Bull. A.M.S. 38(4), 435–465 (2001)

F. Castell, Asymptotic expansion of stochastic flows. Probab. Theor. Relat. Field 96, 225–239 (1993)CrossRefMathSciNetMATH

E.T. Copson, Asymptotic Expansions (Cambridge University Press, Cambridge, 1965)CrossRefMATH

T. Chan, D.S. Dean, K.M. Jansons, L.C.G. Rogers, On polymer conformations in elongational flows. Commun. Math. Phys. 160, 239–257 (1994)CrossRefMathSciNetMATH

F. Delarue, S. Menozzi, Density estimates for a random noise propagating through a chain of differential equations. J. Funct. Anal. 259, 1577–1630 (2010)CrossRefMathSciNetMATH

10.

R.M. Dudley, Lorentz-invariant Markov processes in relativistic phase space. Arkiv för Matematik 6(14), 241–268 (1965)MathSciNet

11.

A.F.M. ter Elst, D.W. Robinson, A. Sikora, Small time asymptotics of diffusion processes. J. Evol. Equ. 7(1), 79–112 (2007)CrossRefMathSciNetMATH

12.

J. Franchi, Y. Le Jan, Relativistic diffusions and schwarzschild geometry. Commun. Pure Appl. Math. LX(2), 187–251 (2007)

13.

J. Franchi, Y. Le Jan, Curvature diffusions in general relativity. Commun. Math. Phys. 307(2), 351–382 (2011)CrossRefMATH

14.

J. Franchi, Y. Le Jan, Hyperbolic Dynamics and Brownian Motion. Oxford Mathematical Monographs (Oxford Science, Oxford, 2012)CrossRefMATH

15.

R. Léandre, Intégration dans la fibre associée à une diffusion dégénérée. Probab. Theor. Relat. Field 76(3), 341–358 (1987)CrossRefMATH

16.

A. Nagel, E.M. Stein, S. Wainger, Balls and metrics defined by vector fields I : Basic properties. Acta Math. 155, 103–147 (1985)

17.

C. Tardif, A Poincaré cone condition in the Poincaré group. Pot. Anal. 38(3), 1001–1030 (2013)CrossRefMathSciNetMATH

18.

S.R.S. Varadhan, Diffusion processes in a small time interval. Commun. Pure Appl. Math. 20, 659–685 (1967)CrossRefMathSciNetMATH

19.

M. Yor, Some Aspects of Brownian Motion. Part I. Some Special Functionals. Lectures in Mathematics, E.T.H. Zürich (Birkhäuser Verlag, Basel, 1992)

Title: Small Time Asymptotics for an Example of Strictly Hypoelliptic Heat Kernel
Author: Jacques Franchi
Publisher: Springer International Publishing
Book: Séminaire de Probabilités XLVI
Print ISBN: 978-3-319-11969-4

Electronic ISBN: 978-3-319-11970-0

Copyright Year: 2014
DOI: https://doi.org/10.1007/978-3-319-11970-0_4