The inviscid burgers equation with Brownian initial velocity

Communications in Mathematical Physics

Volumn 193, Issue 2, 1998, Pages 397-406

  Bertoin, Jean ^a  

^a University of Paris VII LPSM partially supported by ERC Starting Grant 680275 MALIG   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032478424     PISSN: 00103616     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002200050334     Document Type: Article

References (22)

1. Aspandiiarov, S. and Le Gall, J.F.: Some new classes of exceptional times of linear Brownian motion. Ann. Probab. 23, 1605-1626 (1995)
2. Avellaneda, M. and E, W.: Statistical properties of shocks in Burgers turbulence. Commun. Math. Phys. 172, 13-38 (1995)
3. Avellaneda, M.: Statistical properties of shocks in Burgers turbulence, II: Tail probabilities for velocities, shock-strengths and rarefaction intervals. Commun. Math. Phys. 169, 45-59 (1995)
4. Bertoin, J.: Lévy processes. Cambridge: Cambridge University Press, 1996
5. Burgers, J.M.: The nonlinear diffusion equation. Dordrecht: Reidel, 1974
6. Carraro, L. and Duchon, J.: Equation de Burgers avec conditions initiales àaccroissements indépendants et homogènes. Ann. Inst. Henri Poincaré: Analyse non-linéaire (to appear). Results announced in C. R. Acad. Sc. Paris Math. 319, 855-858 (1994)
7. Carraro, L. and Duchon, J.: Equation de Burgers avec conditions initiales àaccroissements indépendants et homogènes. Ann. Inst. Henri Poincaré: Analyse non-linéaire (to appear). Results announced in C. R. Acad. Sc. Paris Math. 319, 855-858 (1994)
8. Fristedt, B.E.: Sample functions of stochastic processes with stationary, independent increments. In: Advances in Probability 3, New-York: Dekker, 1974, pp. 241-396
9. Fristedt, B.E. and Pruitt, W.E.: Lower functions for increasing random walks and subordinators. Z. Wahrscheinlichkeitstheorie verw. Gebiete 18, 167-182 (1971)
10. Fristedt, B.E. and Taylor, S.J.: The packing measure of a general subordinator. Probab. Theory Relat. Fields 92, 493-510 (1992)
11. Getoor, R.K.: Splitting times and shift functional. Z. Wahrscheinlichkeitstheorie verw. Gebiete 47, 69-81 (1979)
12. Hawkes, J.: On the Hausdorff dimension of the intersection of the range of a stable process with a Borel set. Z. Wahrscheinlichkeitstheorie verw. Gebiete 19, 90-102 (1971)
13. Hawkes, J.: On the potential theory of subordinators. Z. Wahrscheinlichkeitstheorie verw. Gebiete 33, 113-132 (1975)
14. xx. Comm. Pure Appl. Math. 3, 201-230 (1950)
15. Jaffard, S.: The multifractal nature of Lévy processes. Preprint
16. Lachal, A.: Sur la distribution de certaines fonctionnelles de l'intégrale du mouvement brownien avec dérive parabolique et cubique. Comm. Pure Appl. Math. XLIX-12, 1299-1338 (1997)
17. Orey, S.: Polar sets for processes with stationary independent increments. Markov processes and potential theory. New-York: Wiley, 1967, pp. 117-126
18. Revuz, D. and Yor, M.: Continuous martingales and Brownian motion. 2nd edn. Berlin: Springer, 1994
19. She, Z.S., Aurell, E. and Frisch, U.: The inviscid Burgers equation with initial data of Brownian type. Commun. Math. Phys. 148, 623-641 (1992)
20. Sinai, Ya.: Statistics of shocks in solution of inviscid Burgers equation. Commun. Math. Phys. 148, 601-621 (1992)
21. Taylor, S.J.: The measure theory of random fractals. Math. Proc. Camb. philos. Soc. 100, 383-406 (1986)
22. Taylor, S.J. and Wendel, J.G.: The exact Hausdorff measure of the zero set of a stable process. Z. Wahrscheinlichkeitstheorie verw. Gebiete 6, 170-180 (1966)