Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations

B. Jourdain

ESAIM: Probability and Statistics (1997)

  • Volume: 1, page 339-355
  • ISSN: 1292-8100

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Jourdain, B.. "Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations." ESAIM: Probability and Statistics 1 (1997): 339-355. <http://eudml.org/doc/104238>.

@article{Jourdain1997,
author = {Jourdain, B.},
journal = {ESAIM: Probability and Statistics},
keywords = {martingale problems; identity diffusion matrix; Lipschitz continuous matrices; Burgers' equation},
language = {eng},
pages = {339-355},
publisher = {EDP Sciences},
title = {Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations},
url = {http://eudml.org/doc/104238},
volume = {1},
year = {1997},
}

TY - JOUR
AU - Jourdain, B.
TI - Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations
JO - ESAIM: Probability and Statistics
PY - 1997
PB - EDP Sciences
VL - 1
SP - 339
EP - 355
LA - eng
KW - martingale problems; identity diffusion matrix; Lipschitz continuous matrices; Burgers' equation
UR - http://eudml.org/doc/104238
ER -

References

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  1. BOSSY, M. and TALAY, D. ( 1996). Convergence Rate for the Approximation of the limit law of weakly interact ing particles: Application to the Burgers Equation. Ann. Appl. Prob. 6 818-861. Zbl0860.60038MR1410117
  2. COLE, J. D. ( 1951). On a quasi-linear parabolie equation occuring in aerodynamics. Quart. Appl. Math. 9 225-236. Zbl0043.09902MR42889
  3. FRIEDMAN, A. ( 1975). Stochastic Differential Equations and Applications. Academic Press. Zbl0323.60056
  4. GRAHAM, C. ( 1992). Nonlinear diffusions with jumps. Ann. Inst. Henri Poincaré. 28 393-402. Zbl0756.60098MR1183993
  5. HOPF, E. ( 1950). The partial differential equation ut + uux = µuxx. Comm. Pure Appl. Math. 3 201-230. Zbl0039.10403MR47234
  6. KARATZAS, I. and SHREVE, S. E. ( 1988). Brownian Motion and Stochastic Calculus. Springer-Verlag. Zbl0638.60065MR917065
  7. MÉLÉARD, S. and ROELLY-COPPOLETTA, S. ( 1987). A propagation of chaos result for a system of particles with moderate interaction. Stochastic Processes and their Application. 26 317-332. Zbl0633.60108MR923112
  8. MEYER, P. A. ( 1966). Probabilités et Potentiel. Hermann. Zbl0138.10402MR205287
  9. OELSCHLÄGER, K. ( 1985). A law of large numbers for moderately interacting diffusion processes. Z. Wahrsch. Verw, Geb. 69 279-322. Zbl0549.60071MR779460
  10. SZNITMAN, A. S. ( 1991). Topics in propagation of chaos. École d'été de probabilités de Saint-Flour XIX - 1989. Lect. Notes in Math, 1464. Springer-Verlag. Zbl0732.60114MR1108185

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