Existence and regularity of a solution of a Kac equation without cutoff using the stochastic calculus of variations

Communications in Mathematical Physics

Volumn 205, Issue 3, 1999, Pages 551-569

  Graham, Carl ^a   Méléard, Sylvie ^b,c  

^a CENTRE DE MATHÉMATIQUES APPLIQUÉES   (France)

^b UNIVERSITÉ PARIS OUEST NANTERRE LA DÉFENSE   (France)

^c SORBONNE UNIVERSITÉ   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033474588     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050689     Document Type: Article

References (14)

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3. 3. Bismut, J.M.: Martingales, the Malliavin Calculus and Hypoellipticity under general Hormander's conditions. Z.W. 56,469-505 (1981)
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8. 8. Diperna, R.J., Lions, P-L.: On the Cauchy problem for Boltzmann equations, global existence and weak stability. Ann. Math. 130, 321-366 (1989)
9. 9. Gabetta, E., Pareschi, L.: About the non cut-off Kac equation: uniqueness and asymptotic behaviour. Comm. Appl. Nonlinear Anal. 4, 1-20 (1997)
10. 10. Jacod, J. , Shiryaev, A.N.: Limit theorems for stochastic processes Berlin-Heidelberg-New York: Springer-Verlag, 1987
11. 11. Nualart, D.: The Malliavin calculus and related topics. Berlin-Heidelberg-New York: Springer-Verlag, 1995
12. 12. Tanaka, H.: Probabilistic treatment of the Boltzmann equation of Maxwellian molecules. Z. Wahrsch. Verw. Geb. 46, 67-105 (1978)
13. 2AN Mathematical Modelling and Numerical Analysis, Vol. 32, n6, 763-772 (1998)
14. 14. Toscani, G., Villani, C.: Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas. J. Stat. Phys. 94, 619-637 (1999)