Dr. Carl Graham

Personal

Prefix: Dr.
First Name: Carl
Last Name: Graham

Education

Degree: B.S.
Major: Probablity

Degree: M.S.

Degree: Ph.D.
Major: Probablity

Summary

Dr. Graham has written at least 17 papers on Applied Probability

Biography

Birthplace: Arlington, Massachusettes

Employment: Professor at the Centre National pour la Recherche Scientifique (CNRS) at the École Polytechnique, Palaiseau , France (CNRS is loosely translated into France's National Center for Scientific Research)

Carl Graham was born in the U.S. but when he was six his father Eugene Alexander Graham, Jr., a mathematician, moved away from a rascist U.S.A. to France, where Carl was raised. Carl's undergraduate education occured at Ecole Normale Superieure (Paris) and Universite Paris 6 (Paris). He received his Masters degree in Mathematics from École Normale Superieure (Paris) and his Ph.D. (1984) in Probability from Universite Paris 6 (Paris).

                                  Research

Dr. Graham has written at least 17 papers on Applied Probability:

17. Graham, C.; Méléard, S. A large deviation principle for a large star-shaped loss network with links of capacity one . Statistical mechanics of large networks (Rocquencourt, 1996). Markov Process. Related Fields 3 (1997), no. 4, 475--492.

16. Graham, C.; Méléard, S. An upper bound of large deviations for a generalized star-shaped loss network . Markov Process. Related Fields 3 (1997), no. 2, 199--223.

15. Graham, Carl; Méléard, Sylvie Stochastic particle approximations for generalized Boltzmann models and convergence estimates . Ann. Probab. 25 (1997), no. 1, 115--132.

14. Graham, C.; Kurtz, Th. G.; Méléard, S.; Protter, Ph. E.; Pulvirenti, M.; Talay, D. Probabilistic models for nonlinear partial differential equations . Lectures given at the 1st Session and Summer Schoolheld in Montecatini Terme, May 22--30, 1995. Edited by Talay and L. Tubaro. Lecture Notes in Mathematics, 1627. Fondazione C.I.M.E.. [C.I.M.E. Foundation] Springer-Verlag, Berlin; Centro Internazionale Matematico Estivo (C.I.M.E.), Florence, 1996. x+301 pp. ISBN: 3-540-61397-8 60-06 (00B25)

13. Graham, Carl; Méléard, Sylvie Convergence rate on path space for stochastic particle approximations to the Boltzmann equation .ICIAM/GAMM 95 (Hamburg, 1995). Z. Angew. Math. Mech. 76 (1996), suppl. 1, 291--294.

12. Graham, Carl A statistical physics approach to large networks . Probabilistic models for nonlinear partial differential equations(Montecatini Terme, 1995), 127--147, Lecture Notes in Math., 1627, Springer, Berlin, 1996.

11. Graham, Carl; Méléard, Sylvie Dynamic asymptotic results for a generalized star-shaped loss network . Ann. Appl. Probab. 5 (1995), no. 3, 666--680.

10. Graham, Carl Homogenization and propagation of chaos to a nonlinear diffusion with sticky reflection. Probab. Theory Related Fields 101 (1995), no. 3, 291--302.

9. Graham, Carl; Méléard, Sylvie Fluctuations for a fully connected loss network with alternate routing. Stochastic Process. Appl. 53 (1994), no. 1, 97--115.

8. Graham, Carl; Méléard, Sylvie Chaos hypothesis for a system interacting through shared resources. Probab. Theory Related Fields 100 (1994), no. 2, 157--173.

7. Graham, Carl; Méléard, Sylvie Propagation of chaos for a fully connected loss network with alternate routing. Stochastic Process. Appl. 44 (1993), no. 1, 159--180.

6. Graham, Carl Nonlinear diffusion with jumps. Ann. Inst. H. Poincaré Probab. Statist. 28 (1992), no. 3, 393--402.

5. Graham, Carl; McKean-Vlasov Itô-Skorohod equations, and nonlinear diffusions with discrete jump sets. Stochastic Process. Appl. 40 (1992), no. 1, 69--82.

4. Graham, Carl Nonlinear limit for a system of diffusing particles which alternate between two states. Appl. Math. Optim. 22 (1990), no. 1, 75--90.

3. Graham, Carl; Métivier, Michel System of interacting particles and nonlinear diffusion reflecting in a domain with sticky boundary. Probab. Theory Related Fields 82 (1989), no. 2, 225--240.

2. Graham, Carl The martingale problem with sticky reflection conditions, and a system of particles interacting at the boundary. Ann. Inst. H. Poincaré Probab. Statist. 24 (1988), no. 1, 45--72.

1. Graham, Carl Boundary processes: the calculus of processes diffusing on the boundary. Ann. Inst. H. Poincaré Probab. Statist. 21 (1985), no. 1, 73--102.