-
2
-
-
84990619144
-
Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation
-
doi:10.1002/cpa.3160460503
-
Bardos C, Golse F, Levermore CD (1993) Fluid dynamic limits of kinetic equations. II. Convergence proofs for the Boltzmann equation. Commun Pure Appl Math 46(5): 667-753. doi: 10. 1002/cpa. 3160460503.
-
(1993)
Commun Pure Appl Math
, vol.46
, Issue.5
, pp. 667-753
-
-
Bardos, C.1
Golse, F.2
Levermore, C.D.3
-
3
-
-
0001076950
-
Fluid dynamic limits of kinetic equations. I. Formal derivations
-
doi: 10. 1007/BF01026608
-
Bardos C, Golse F, Levermore D (1991) Fluid dynamic limits of kinetic equations. I. Formal derivations. J Stat Phys 63(1-2): 323-344. doi: 10. 1007/BF01026608.
-
(1991)
J Stat Phys
, vol.63
, Issue.1-2
, pp. 323-344
-
-
Bardos, C.1
Golse, F.2
Levermore, D.3
-
4
-
-
0037603583
-
Deterministic approximation of stochastic evolution in games
-
doi:10.1111/1468-0262.00429
-
Benaim M, Weibull JW (2003) Deterministic approximation of stochastic evolution in games. Econometrica 71(3): 873-903. doi: 10. 1111/1468-0262. 00429.
-
(2003)
Econometrica
, vol.71
, Issue.3
, pp. 873-903
-
-
Benaim, M.1
Weibull, J.W.2
-
7
-
-
38249007930
-
Laws of large numbers for dynamic-systems with randomly matched individuals
-
doi:10.1016/0022-0531(92)90046-K
-
Boylan RT (1992) Laws of large numbers for dynamic-systems with randomly matched individuals. J Econ Theory 57(2): 473-504. doi: 10. 1016/0022-0531(92)90046-K.
-
(1992)
J Econ Theory
, vol.57
, Issue.2
, pp. 473-504
-
-
Boylan, R.T.1
-
8
-
-
0010970766
-
Continuous approximation of dynamical-systems with randomly matched individuals
-
doi: 10. 1006/jeth. 1995. 1060
-
Boylan RT (1995) Continuous approximation of dynamical-systems with randomly matched individuals. J Econ Theory 66(2): 615-625. doi: 10. 1006/jeth. 1995. 1060.
-
(1995)
J Econ Theory
, vol.66
, Issue.2
, pp. 615-625
-
-
Boylan, R.T.1
-
10
-
-
67649306446
-
The Boltzmann equation and fluid dynamics
-
North-Holland, Amsterdam
-
Cercignani C (2002) The Boltzmann equation and fluid dynamics. Handbook of mathematical fluid dynamics, vol I. North-Holland, Amsterdam, pp 1-69.
-
(2002)
Handbook of mathematical fluid dynamics, vol I
, pp. 1-69
-
-
Cercignani, C.1
-
11
-
-
3042580676
-
Kinetic models for chemotaxis and their drift-diffusion limits
-
doi:10.1007/s00605-004-0234-7
-
Chalub FACC, Markowich PA, Perthame B, Schmeiser C (2004) Kinetic models for chemotaxis and their drift-diffusion limits. Monatsh Math 142(1-2): 123-141. doi: 10. 1007/s00605-004-0234-7.
-
(2004)
Monatsh Math
, vol.142
, Issue.1-2
, pp. 123-141
-
-
Chalub, F.A.C.C.1
Markowich, P.A.2
Perthame, B.3
Schmeiser, C.4
-
12
-
-
70449112711
-
From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics
-
doi:10.1016/j.tpb.2009.08.006
-
Chalub FACC, Souza MO (2009) From discrete to continuous evolution models: a unifying approach to drift-diffusion and replicator dynamics. Theor Popul Biol 76(4): 268-277. doi: 10. 1016/j. tpb. 2009. 08. 006.
-
(2009)
Theor Popul Biol
, vol.76
, Issue.4
, pp. 268-277
-
-
Chalub, F.A.C.C.1
Souza, M.O.2
-
13
-
-
70350443026
-
A non-standard evolution problem arising in population genetics
-
Chalub FACC, Souza MO (2009b) A non-standard evolution problem arising in population genetics. Commun Math Sci 7(2): 489-502.
-
(2009)
Commun Math Sci
, vol.7
, Issue.2
, pp. 489-502
-
-
Chalub, F.A.C.C.1
Souza, M.O.2
-
14
-
-
79951579897
-
The SIR epidemic model from a PDE point of view
-
doi:10.1016/j.mcm.2010.05.036
-
Chalub FACC, Souza MO (2011) The SIR epidemic model from a PDE point of view. Math Comput Model 53(7-8): 1568-1574. doi: 10. 1016/j. mcm. 2010. 05. 036.
-
(2011)
Math Comput Model
, vol.53
, Issue.7-8
, pp. 1568-1574
-
-
Chalub, F.A.C.C.1
Souza, M.O.2
-
15
-
-
33645741606
-
Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models
-
doi:10.1016/j.tpb.2005.10.004
-
Champagnat N, Ferrière R, Méléard S (2006) Unifying evolutionary dynamics: from individual stochastic processes to macroscopic models. Theor Popul Biol 69(3): 297-321. doi: 10. 1016/j. tpb. 2005. 10. 004.
-
(2006)
Theor Popul Biol
, vol.69
, Issue.3
, pp. 297-321
-
-
Champagnat, N.1
Ferrière, R.2
Méléard, S.3
-
16
-
-
55849103220
-
From individual stochastic processes to macroscopic models in adaptive evolution
-
doi:10.1080/15326340802437710
-
Champagnat N, Ferrière R, Méléard S (2008) From individual stochastic processes to macroscopic models in adaptive evolution. Stoch Models 24(suppl. 1): 2-44. doi: 10. 1080/15326340802437710.
-
(2008)
Stoch Models
, vol.24
, Issue.SUPPL. 1
, pp. 2-44
-
-
Champagnat, N.1
Ferrière, R.2
Méléard, S.3
-
17
-
-
0010919918
-
Dirac and Klein-Gordon equations: convergence of solutions in the nonrelativistic limit
-
Cirincione RJ, Chernoff PR (1981) Dirac and Klein-Gordon equations: convergence of solutions in the nonrelativistic limit. Commun Math Phys 79(1): 33-46.
-
(1981)
Commun Math Phys
, vol.79
, Issue.1
, pp. 33-46
-
-
Cirincione, R.J.1
Chernoff, P.R.2
-
18
-
-
0042260644
-
Continuous approximations of stochastic evolutionary game dynamics
-
doi:10.1006/jeth.1999.2596
-
Corradi V, Sarin R (2000) Continuous approximations of stochastic evolutionary game dynamics. J Econ Theory 94(2): 163-191. doi: 10. 1006/jeth. 1999. 2596.
-
(2000)
J Econ Theory
, vol.94
, Issue.2
, pp. 163-191
-
-
Corradi, V.1
Sarin, R.2
-
20
-
-
84967708673
-
User's guide to viscosity solutions of second order partial differential equations
-
doi:10.1090/S0273-0979-1992-00266-5
-
Crandall MG, Ishii H, Lions PL (1992) User's guide to viscosity solutions of second order partial differential equations. Bull AMS 27(1): 1-67. doi: 10. 1090/S0273-0979-1992-00266-5.
-
(1992)
Bull AMS
, vol.27
, Issue.1
, pp. 1-67
-
-
Crandall, M.G.1
Ishii, H.2
Lions, P.L.3
-
22
-
-
0002306354
-
Ordinary differential equations, transport theory and sobolev spaces
-
doi:10.1007/BF01393835
-
DiPerna RJ, Lions PL (1989) Ordinary differential equations, transport theory and sobolev spaces. Invent Math 98: 511-547. doi: 10. 1007/BF01393835.
-
(1989)
Invent Math
, vol.98
, pp. 511-547
-
-
DiPerna, R.J.1
Lions, P.L.2
-
25
-
-
0003448545
-
-
2nd edn., Providence: American Mathematical Society
-
Evans LC (2010) Partial differential equations, 2nd edn. American Mathematical Society, Providence.
-
(2010)
Partial Differential Equations
-
-
Evans, L.C.1
-
28
-
-
0001077472
-
On the dominance ratio
-
doi:10.1007/BF02459576
-
Fisher RA (1922) On the dominance ratio. Proc R Soc Edinb 42: 321-341. doi: 10. 1007/BF02459576.
-
(1922)
Proc R Soc Edinb
, vol.42
, pp. 321-341
-
-
Fisher, R.A.1
-
29
-
-
0001122789
-
The distribution of gene ratios for rare mutations
-
Fisher RA (1930) The distribution of gene ratios for rare mutations. Proc R Soc Edinb 50: 214-219.
-
(1930)
Proc R Soc Edinb
, vol.50
, pp. 214-219
-
-
Fisher, R.A.1
-
30
-
-
0001294377
-
Stochastic evolutionary game dynamics
-
doi:10.1016/0040-5809(90)90011-J
-
Foster D, Young P (1990) Stochastic evolutionary game dynamics. Theor Popul Biol 38(2): 219-232. doi: 10. 1016/0040-5809(90)90011-J.
-
(1990)
Theor Popul Biol
, vol.38
, Issue.2
, pp. 219-232
-
-
Foster, D.1
Young, P.2
-
31
-
-
26844479973
-
A microscopic probabilistic description of a locally regulated population and macroscopic approximations
-
doi:10.1214/105051604000000882
-
Fournier N, Méléard S (2004) A microscopic probabilistic description of a locally regulated population and macroscopic approximations. Ann Appl Probab 14(4): 1880-1919. doi: 10. 1214/105051604000000882.
-
(2004)
Ann Appl Probab
, vol.14
, Issue.4
, pp. 1880-1919
-
-
Fournier, N.1
Méléard, S.2
-
32
-
-
0001129788
-
Evolutionary dynamics with aggregate shocks
-
doi:10.1016/0022-0531(92)90044-I
-
Fudenberg D, Harris C (1992) Evolutionary dynamics with aggregate shocks. J Econ Theory 57(2): 420-441. doi: 10. 1016/0022-0531(92)90044-I.
-
(1992)
J Econ Theory
, vol.57
, Issue.2
, pp. 420-441
-
-
Fudenberg, D.1
Harris, C.2
-
34
-
-
33846791634
-
The classical limit for quantum mechanical correlation functions
-
Hepp K (1974) The classical limit for quantum mechanical correlation functions. Commun Math Phys 35: 265-277.
-
(1974)
Commun Math Phys
, vol.35
, pp. 265-277
-
-
Hepp, K.1
-
35
-
-
0034917420
-
The diffusion limit of transport equations derived from velocity-jump processes
-
(electronic). doi: 10. 1137/S0036139999358167
-
Hillen T, Othmer HG (2000) The diffusion limit of transport equations derived from velocity-jump processes. SIAM J Appl Math 61(3): 751-775 (electronic). doi: 10. 1137/S0036139999358167.
-
(2000)
SIAM J Appl Math
, vol.61
, Issue.3
, pp. 751-775
-
-
Hillen, T.1
Othmer, H.G.2
-
37
-
-
33645974834
-
Evolutionary game dynamics in a Wright-Fisher process
-
doi:10.1007/s00285-005-0369-8
-
Imhof LA, Nowak MA (2006) Evolutionary game dynamics in a Wright-Fisher process. J Math Biol 52(5): 667-681. doi: 10. 1007/s00285-005-0369-8.
-
(2006)
J Math Biol
, vol.52
, Issue.5
, pp. 667-681
-
-
Imhof, L.A.1
Nowak, M.A.2
-
41
-
-
0000800333
-
On the probability of fixation of mutant genes in a population
-
Kimura M (1962) On the probability of fixation of mutant genes in a population. Genetics 47: 713-719.
-
(1962)
Genetics
, vol.47
, pp. 713-719
-
-
Kimura, M.1
-
42
-
-
22144485943
-
Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory
-
doi:10.1016/j.tpb.2005.04.001
-
Lessard S (2005) Long-term stability from fixation probabilities in finite populations: new perspectives for ESS theory. Theor Popul Biol 68(1): 19-27. doi: 10. 1016/j. tpb. 2005. 04. 001.
-
(2005)
Theor Popul Biol
, vol.68
, Issue.1
, pp. 19-27
-
-
Lessard, S.1
-
43
-
-
34248388067
-
The probability of fixation of a single mutant in an exchangeable selection model
-
doi:10.1007/s00285-007-0069-7
-
Lessard S, Ladret V (2007) The probability of fixation of a single mutant in an exchangeable selection model. J Math Biol 54: 721-744. doi: 10. 1007/s00285-007-0069-7.
-
(2007)
J Math Biol
, vol.54
, pp. 721-744
-
-
Lessard, S.1
Ladret, V.2
-
46
-
-
34447512608
-
Singular solutions of the diffusion equation of population genetics
-
doi:10.1016/j.jtbi.2007.04.016
-
McKane AJ, Waxman D (2007) Singular solutions of the diffusion equation of population genetics. J Theor Biol 247(4): 849-858. doi: 10. 1016/j. jtbi. 2007. 04. 016.
-
(2007)
J Theor Biol
, vol.247
, Issue.4
, pp. 849-858
-
-
McKane, A.J.1
Waxman, D.2
-
47
-
-
84877759353
-
Quasi-stationary distributions and population processes
-
doi:10.1214/11-PS191
-
Méléard S, Villemonais D (2012) Quasi-stationary distributions and population processes. Probab Surv 9: 340-410. doi: 10. 1214/11-PS191.
-
(2012)
Probab Surv
, vol.9
, pp. 340-410
-
-
Méléard, S.1
Villemonais, D.2
-
48
-
-
84871941090
-
Thoughts on the geometry of meso-evolution: collecting mathematical elements for a post-modern synthesis
-
In: Chalub FACC, Rodrigues JF (eds). Springer, Basel
-
Metz JAJ (2011) Thoughts on the geometry of meso-evolution: collecting mathematical elements for a post-modern synthesis. In: Chalub FACC, Rodrigues JF (eds) The mathematics of Darwin's legacy. Springer, Basel, pp 193-231.
-
(2011)
The mathematics of Darwin's legacy
, pp. 193-231
-
-
Metz, J.A.J.1
-
51
-
-
0036553052
-
The diffusion limit of transport equations. II. Chemotaxis equations
-
(electronic). doi: 10. 1137/S0036139900382772
-
Othmer HG, Hillen T (2002) The diffusion limit of transport equations. II. Chemotaxis equations. SIAM J Appl Math 62(4): 1222-1250 (electronic). doi: 10. 1137/S0036139900382772.
-
(2002)
SIAM J Appl Math
, vol.62
, Issue.4
, pp. 1222-1250
-
-
Othmer, H.G.1
Hillen, T.2
-
52
-
-
0003617670
-
-
Cambridge University Press, Cambridge
-
Rogers L, Williams D (2000a) Diffusions, Markov processes, and martingales, Foundations, vol 1. Cambridge University Press, Cambridge.
-
(2000)
Diffusions, Markov processes, and martingales, Foundations, vol 1
-
-
Rogers, L.1
Williams, D.2
-
53
-
-
0003617670
-
-
Cambridge University Press, Cambridge
-
Rogers L, Williams D (2000b) Diffusions, Markov processes and martingales, Itô calculus, vol 2. Cambridge University Press, Cambridge.
-
(2000)
Diffusions, Markov processes and martingales, Itô calculus
, vol.2
-
-
Rogers, L.1
Williams, D.2
-
54
-
-
84972527761
-
Class of Markov-chains related to selection in population-genetics
-
Sato KI (1976) Class of Markov-chains related to selection in population-genetics. J Math Soc Japan 28(4): 621-637.
-
(1976)
J Math Soc Japan
, vol.28
, Issue.4
, pp. 621-637
-
-
Sato, K.I.1
-
55
-
-
0039514624
-
Convergence to a diffusion of a multi-allelic model in population genetics
-
Sato KI (1978) Convergence to a diffusion of a multi-allelic model in population genetics. Adv Appl Probab 10(3): 538-562.
-
(1978)
Adv Appl Probab
, vol.10
, Issue.3
, pp. 538-562
-
-
Sato, K.I.1
-
56
-
-
84897620596
-
Limit diffusions of some stepping-stone models
-
Sato KI (1983) Limit diffusions of some stepping-stone models. J Appl Probab 20(3): 460-471.
-
(1983)
J Appl Probab
, vol.20
, Issue.3
, pp. 460-471
-
-
Sato, K.I.1
-
58
-
-
32644457962
-
Can a mixed strategy be stable in a finite population?
-
doi:10.1016/S0022-5193(88)80100-0
-
Smith JM (1988) Can a mixed strategy be stable in a finite population? J Theor Biol 130(2): 247-251. doi: 10. 1016/S0022-5193(88)80100-0.
-
(1988)
J Theor Biol
, vol.130
, Issue.2
, pp. 247-251
-
-
Smith, J.M.1
-
60
-
-
0034455986
-
The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems
-
(electronic). doi: 10. 1137/S0036139998342065
-
Stevens A (2000) The derivation of chemotaxis equations as limit dynamics of moderately interacting stochastic many-particle systems. SIAM J Appl Math 61(1): 183-212 (electronic). doi: 10. 1137/S0036139998342065.
-
(2000)
SIAM J Appl Math
, vol.61
, Issue.1
, pp. 183-212
-
-
Stevens, A.1
-
64
-
-
28844506643
-
Coevolutionary dynamics: from finite to infinite populations
-
doi:10.1103/PhysRevLett.95.238701
-
Traulsen A, Claussen JC, Hauert C (2005) Coevolutionary dynamics: from finite to infinite populations. Phys Rev Lett 95(23): 238701. doi: 10. 1103/PhysRevLett. 95. 238701.
-
(2005)
Phys Rev Lett
, vol.95
, Issue.23
, pp. 238701
-
-
Traulsen, A.1
Claussen, J.C.2
Hauert, C.3
-
65
-
-
84859587996
-
Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
-
doi: 10. 1103/PhysRevE. 85. 041901
-
Traulsen A, Claussen JC, Hauert C (2012) Stochastic differential equations for evolutionary dynamics with demographic noise and mutations. Phys Rev E 85(4, Part 1). doi: 10. 1103/PhysRevE. 85. 041901.
-
(2012)
Phys Rev E
, vol.85
, Issue.4 PART 1
-
-
Traulsen, A.1
Claussen, J.C.2
Hauert, C.3
-
67
-
-
0242530453
-
Can a mixed strategy be stable in a finite population?-reply
-
doi:10.1016/S0022-5193(88)80222-4
-
Vickery WL (1988) Can a mixed strategy be stable in a finite population?-reply. J Theor Biol 132(3): 375-378. doi: 10. 1016/S0022-5193(88)80222-4.
-
(1988)
J Theor Biol
, vol.132
, Issue.3
, pp. 375-378
-
-
Vickery, W.L.1
-
68
-
-
77958602332
-
Comparison and content of the Wright-Fisher model of random genetic drift, the diffusion approximation, and an intermediate model
-
doi:10.1016/j.jtbi.2010.10.014
-
Waxman D (2011) Comparison and content of the Wright-Fisher model of random genetic drift, the diffusion approximation, and an intermediate model. J Theor Biol 269(1): 79-87. doi: 10. 1016/j. jtbi. 2010. 10. 014.
-
(2011)
J Theor Biol
, vol.269
, Issue.1
, pp. 79-87
-
-
Waxman, D.1
-
70
-
-
0001111820
-
The distribution of gene frequencies in populations
-
Wright S (1937) The distribution of gene frequencies in populations. Proc Natl Acad Sci USA 23: 307-320.
-
(1937)
Proc Natl Acad Sci USA
, vol.23
, pp. 307-320
-
-
Wright, S.1
-
71
-
-
0001111819
-
The distribution of gene frequencies under irreversible mutations
-
Wright S (1938) The distribution of gene frequencies under irreversible mutations. Proc Natl Acad Sci USA 24: 253-259.
-
(1938)
Proc Natl Acad Sci USA
, vol.24
, pp. 253-259
-
-
Wright, S.1
|