-
1
-
-
33744775760
-
Asymptotic analysis ofmultiscale approximations to reaction networks
-
MR2288709
-
BALL, K., KURTZ, T. G., POPOVIC, L. and REMPALA, G. (2006). Asymptotic analysis ofmultiscale approximations to reaction networks. Ann. Appl. Probab. 16 1925-1961. MR2288709
-
(2006)
Ann. Appl. Probab.
, vol.16
, pp. 1925-1961
-
-
Ball, K.1
Kurtz, T.G.2
Popovic, L.3
Rempala, G.4
-
2
-
-
22944480262
-
The slow-scale stochastic simulation algorithm
-
CAO, Y., GILLESPIE, D. T. and PETZOLD, L. R. (2005). The slow-scale stochastic simulation algorithm. J. Chem. Phys. 122 014116. Available at http://link.aip.org/link/?JCP/122/014116/1.
-
(2005)
J. Chem. Phys.
, vol.122
, pp. 014116
-
-
Cao, Y.1
Gillespie, D.T.2
Petzold, L.R.3
-
3
-
-
70449514562
-
Hybrid stochastic simplifications for multiscale gene networks
-
CRUDU, A., DEBUSSCHE, A. and RADULESCU, O. (2009). Hybrid stochastic simplifications for multiscale gene networks. BMC Syst. Biol. 3 89.
-
(2009)
BMC Syst. Biol.
, vol.3
, pp. 89
-
-
Crudu, A.1
Debussche, A.2
Radulescu, O.3
-
4
-
-
84879765389
-
A pseudo-steady state approximation for stochastic chemical kinetics
-
MR0517973
-
DARDEN, T. (1979). A pseudo-steady state approximation for stochastic chemical kinetics. Rocky Mountain J. Math. 9 51-71. MR0517973
-
(1979)
Rocky Mountain J. Math.
, vol.9
, pp. 51-71
-
-
Darden, T.1
-
5
-
-
84879772305
-
Enzyme kinetics: Stochastic vs. deterministic models
-
Austin, Tex., 1980, Univ. Texas Press, Austin, TX. MR0774792
-
DARDEN, T. A. (1982). Enzyme kinetics: Stochastic vs. deterministic models. In Instabilities, Bifurcations, and Fluctuations in Chemical Systems (Austin, Tex., 1980) 248-272. Univ. Texas Press, Austin, TX. MR0774792
-
(1982)
Instabilities, Bifurcations, and Fluctuations in Chemical Systems
, pp. 248-272
-
-
Darden, T.A.1
-
7
-
-
27744516835
-
Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates
-
E, W., LIU, D. and VANDEN-EIJNDEN, E. (2005). Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates. J. Chem. Phys. 123 194107. Available at http://link.aip.org/link/?JCP/123/194107/1.
-
(2005)
J. Chem. Phys.
, vol.123
, pp. 194107
-
-
Liu D, E.W.1
Vanden-Eijnden, E.2
-
8
-
-
33846123314
-
Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales
-
MR2290567
-
E, W., LIU, D. and VANDEN-EIJNDEN, E. (2007). Nested stochastic simulation algorithms for chemical kinetic systems with multiple time scales. J. Comput. Phys. 221 158-180. MR2290567
-
(2007)
J. Comput. Phys.
, vol.221
, pp. 158-180
-
-
Liu D, E.W.1
Vanden-Eijnden, E.2
-
10
-
-
33645429016
-
Exact stochastic simulation of coupled chemical reactions
-
GILLESPIE, D. T. (1977). Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81 2340-2361.
-
(1977)
J. Phys. Chem.
, vol.81
, pp. 2340-2361
-
-
Gillespie, D.T.1
-
11
-
-
18844402156
-
Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems
-
GOUTSIAS, J. (2005). Quasiequilibrium approximation of fast reaction kinetics in stochastic biochemical systems. J. Chem. Phys. 122 184102. Available at http://link.aip.org/link/?JCP/122/184102/1.
-
(2005)
J. Chem. Phys.
, vol.122
, pp. 184102
-
-
Goutsias, J.1
-
12
-
-
0037109565
-
Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics
-
HASELTINE, E. L. and RAWLINGS, J. B. (2002). Approximate simulation of coupled fast and slow reactions for stochastic chemical kinetics. J. Chem. Phys. 117 6959-6969.
-
(2002)
J. Chem. Phys.
, vol.117
, pp. 6959-6969
-
-
Haseltine, E.L.1
Rawlings, J.B.2
-
13
-
-
74049102425
-
Stochastic kinetic modeling of vesicular stomatitis virus intracellular growth
-
MR2544630
-
HENSEL, S. C., RAWLINGS, J. B. and YIN, J. (2009). Stochastic kinetic modeling of vesicular stomatitis virus intracellular growth. Bull. Math. Biol. 71 1671-1692. MR2544630
-
(2009)
Bull. Math. Biol.
, vol.71
, pp. 1671-1692
-
-
Hensel, S.C.1
Rawlings, J.B.2
Yin, J.3
-
14
-
-
3042567006
-
A non-Skorohod topology on the Skorohod space
-
(electronic). MR1475862
-
JAKUBOWSKI, A. (1997). A non-Skorohod topology on the Skorohod space. Electron. J. Probab. 2 21 pp. (electronic). MR1475862
-
(1997)
Electron. J. Probab.
, vol.2
-
-
Jakubowski, A.1
-
15
-
-
0002263301
-
Weak and strong convergence of distributions of counting processes
-
KABANOV, Y. M., LIPTSER, R. S. and SHIRYAEV, A. N. (1984). Weak and strong convergence of distributions of counting processes. Theory Probab. Appl. 28 303-336.
-
(1984)
Theory Probab. Appl.
, vol.28
, pp. 303-336
-
-
Kabanov, Y.M.1
Liptser, R.S.2
Shiryaev, A.N.3
-
17
-
-
84879756175
-
-
Unpublished manuscript. School of Mathematics, Univ. Minnesota, Dept. Mathematics and Statistics, Univ. Wisconsin, Madison and Dept. Mathematics and Statistics, Concordia Univ
-
KANG, H.-W., KURTZ, T. G. and POPOVIC, L. (2012). Diffusion approximations for multiscale chemical reaction models. Unpublished manuscript. School of Mathematics, Univ. Minnesota, Dept. Mathematics and Statistics, Univ. Wisconsin, Madison and Dept. Mathematics and Statistics, Concordia Univ.
-
(2012)
Diffusion Approximations for Multiscale Chemical Reaction Models
-
-
Kang, H.-W.1
Kurtz, T.G.2
Popovic, L.3
-
18
-
-
0001761643
-
On stochastic processes defined by differential equations with a small parameter
-
KHAS'MINSKIǏ, R. Z. (1966a). On stochastic processes defined by differential equations with a small parameter. Theory Probab. Appl. 11 211-228.
-
(1966)
Theory Probab. Appl.
, vol.11
, pp. 211-228
-
-
Khas'Minskiǐ, R.Z.1
-
19
-
-
0001761644
-
KHAS'MINSKIǏ, R. Z.
-
KHAS'MINSKIǏ, R. Z. (1966b). A limit theorem for the solutions of differential equations with random right-hand sides. Theory Probab. Appl. 11 390-406.
-
(1966)
Theory Probab. Appl.
, vol.11
, pp. 390-406
-
-
-
20
-
-
0001455869
-
The relationship between stochastic and deterministic models for chemical reactions
-
KURTZ, T. G. (1972). The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57 2976-2978.
-
(1972)
J. Chem. Phys.
, vol.57
, pp. 2976-2978
-
-
Kurtz, T.G.1
-
21
-
-
0000660738
-
Strong approximation theorems for density dependent Markov chains
-
MR0464414
-
KURTZ, T. G. (1977/78). Strong approximation theorems for density dependent Markov chains. Stochastic Process. Appl. 6 223-240. MR0464414
-
(1977)
Stochastic Process. Appl.
, vol.6
, pp. 223-240
-
-
Kurtz, T.G.1
-
22
-
-
0010147542
-
Representations of Markov processes as multiparameter time changes
-
MR0577310
-
KURTZ, T. G. (1980). Representations of Markov processes as multiparameter time changes. Ann. Probab. 8 682-715. MR0577310
-
(1980)
Ann. Probab.
, vol.8
, pp. 682-715
-
-
Kurtz, T.G.1
-
23
-
-
0001168654
-
Random time changes and convergence in distribution under the Meyer-Zheng conditions
-
MR1112405
-
KURTZ, T. G. (1991). Random time changes and convergence in distribution under the Meyer-Zheng conditions. Ann. Probab. 19 1010-1034. MR1112405
-
(1991)
Ann. Probab.
, vol.19
, pp. 1010-1034
-
-
Kurtz, T.G.1
-
24
-
-
0004399662
-
Averaging for martingale problems and stochastic approximation
-
(New Brunswick, NJ, 1991). Lecture Notes in Control and Information Sciences, Springer, Berlin. MR1169928
-
KURTZ, T. G. (1992). Averaging for martingale problems and stochastic approximation. In Applied Stochastic Analysis (New Brunswick, NJ, 1991). Lecture Notes in Control and Information Sciences 177 186-209. Springer, Berlin. MR1169928
-
(1992)
Applied Stochastic Analysis
, vol.177
, pp. 186-209
-
-
Kurtz, T.G.1
-
25
-
-
49749098924
-
Multiscale modeling of chemical kinetics via the master equation
-
MR2393029
-
MACNAMARA, S., BURRAGE, K. and SIDJE, R. B. (2007). Multiscale modeling of chemical kinetics via the master equation. Multiscale Model. Simul. 6 1146-1168. MR2393029
-
(2007)
Multiscale Model. Simul.
, vol.6
, pp. 1146-1168
-
-
MacNamara, S.1
Burrage, K.2
Sidje, R.B.3
-
26
-
-
34548474499
-
Two classes of quasi-steadystate model reductions for stochastic kinetics
-
MASTNY, E. A., HASELTINE, E. L. and RAWLINGS, J. B. (2007). Two classes of quasi-steadystate model reductions for stochastic kinetics. J. Chem. Phys. 127 094106. Available at http://link.aip.org/link/?JCP/127/094106/1.
-
(2007)
J. Chem. Phys.
, vol.127
, pp. 094106
-
-
Mastny, E.A.1
Haseltine, E.L.2
Rawlings, J.B.3
-
27
-
-
0001125838
-
Démonstration simplifiée d'un théorème de Knight
-
Springer, Berlin. MR0380972
-
MEYER, P. A. (1971). Démonstration simplifiée d'un théorème de Knight. In Séminaire de Probabilités, V (Univ. Strasbourg, Année Universitaire 1969-1970). Lecture Notes in Math. 191 191-195. Springer, Berlin. MR0380972
-
(1971)
Séminaire de Probabilités, v (Univ. Strasbourg, Année Universitaire 1969-1970). Lecture Notes in Math.
, vol.191
, pp. 191-195
-
-
Meyer, P.A.1
-
29
-
-
0037444724
-
Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm
-
RAO, C. V. and ARKIN, A. P. (2003). Stochastic chemical kinetics and the quasi-steady-state assumption: Application to the Gillespie algorithm. J. Chem. Phys. 118 4999-5010.
-
(2003)
J. Chem. Phys.
, vol.118
, pp. 4999-5010
-
-
Rao, C.V.1
Arkin, A.P.2
-
30
-
-
0024731820
-
The quasi-steady-state assumption: A case study in perturbation
-
MR1012300
-
SEGEL, L. A. and SLEMROD, M. (1989). The quasi-steady-state assumption: A case study in perturbation. SIAM Rev. 31 446-477. MR1012300
-
(1989)
SIAM Rev.
, vol.31
, pp. 446-477
-
-
Segel, L.A.1
Slemrod, M.2
-
31
-
-
0035812883
-
Stochastic kinetic analysis of Escherichia coli stress circuit using sigma(32)-targeted antisense
-
SRIVASTAVA, R., PETERSON, M. S. and BENTLEY, W. E. (2001). Stochastic kinetic analysis of Escherichia coli stress circuit using sigma(32)-targeted antisense. Biotechnol. Bioeng. 75 120-129.
-
(2001)
Biotechnol. Bioeng.
, vol.75
, pp. 120-129
-
-
Srivastava, R.1
Peterson, M.S.2
Bentley, W.E.3
-
32
-
-
74049117430
-
Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes
-
MR2552726
-
ZEISER, S., FRANZ, U. and LIEBSCHER, V. (2010). Autocatalytic genetic networks modeled by piecewise-deterministic Markov processes. J. Math. Biol. 60 207-246. MR2552726
-
(2010)
J. Math. Biol.
, vol.60
, pp. 207-246
-
-
Zeiser, S.1
Franz, U.2
Liebscher, V.3
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