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Decomposition of stochastic flows generated by Stratonovich SDEs with jumps
1. | Department of Mathematics, University of Campinas - UNICAMP, Campinas, 13083-859, Brazil, Brazil, Brazil |
References:
[1] |
D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, 2004.
doi: 10.1017/CBO9780511755323. |
[2] |
J. M. Bismut, Mécanique Aléatoire, Lecture Notes in Math., 866. Springer-Verlag, Berlin-New York, 1981. |
[3] |
P. J. Catuogno, F. B. da Silva and P. R. Ruffino, Decomposition of stochastic flows with automorphism of subbundles component, Stochastics and Dynamics, 12 (2012), 1150013, 15 pp.
doi: 10.1142/S0219493712003705. |
[4] |
P. J. Catuogno, F. B. da Silva and P. R. Ruffino, Decomposition of stochastic flows in manifolds with complementary distributions, Stochastics and Dynamics, 13 (2013), 1350009, 12 pp.
doi: 10.1142/S0219493713500093. |
[5] |
F. Colonius and W. Kliemann, The Dynamics of Control, Systems and Control: Foundations and Applications. Birkhäuser Boston, Inc., Boston, MA, 2000.
doi: 10.1007/978-1-4612-1350-5. |
[6] |
F. Colonius and P. R. Ruffino, Nonlinear Iwasawa decomposition of control flows, Discrete Continuous Dyn. Systems, (Serie A) 18 (2007), 339-354.
doi: 10.3934/dcds.2007.18.339. |
[7] |
I. G. Gargate and P. R. Ruffino, An averaging principle for diffusions in foliated spaces, The Annals of Probab., 44 (2016), 567-588.
doi: 10.1214/14-AOP982. |
[8] |
H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, in: École d'Eté de Probabilités de Saint-Flour XII - 1982, ed. P.L. Hennequin, Lecture Notes on Maths., Springer, 1097 (1984), 143-303.
doi: 10.1007/BFb0099433. |
[9] |
H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge, 1997. |
[10] |
X.-M. Li, An averaging principle for a completely integrable stochastic Hamiltonian system, Nonlinearity, 21 (2008), 803-822.
doi: 10.1088/0951-7715/21/4/008. |
[11] |
T. Kurtz, E. Pardoux and P. Protter, Stratonovich stochastic differential equations driven by general semimartingales, Annales de l'I.H.P., section B, 31 (1995), 351-377. |
[12] |
M. Liao, Decomposition of stochastic flows and Lyapunov exponents, Probab. Theory Rel. Fields, 117 (2000), 589-607.
doi: 10.1007/PL00008736. |
[13] |
J. Milnor, Remarks on infinite dimensional lie groups, In: Relativity, Groups and Topology II, Les Houches Session XL, 1983, North Holland, Amsterdam, 1984, 1007-1057. |
[14] |
K.-H. Neeb, Infinite Dimesional Lie Groups, Monastir Summer Schoool, 2009. Available from hal.archives-ouvertes.fr/docs/00/39/.../CoursKarl-HermannNeeb.pdf. |
[15] |
H. Omori, Infinite Dimensional Lie Groups, Translations of Math Monographs 158, AMS, 1997. |
[16] |
L. Morgado and P. Ruffino, Extension of time for decomposition of stochastic flows in spaces with complementary foliations, Electron. Comm. Probab., 20 (2015), 9pp.
doi: 10.1214/ECP.v20-3762. |
[17] |
P. Ruffino, Decomposition of stochastic flow and rotation matrix, Stochastics and Dynamics, 2 (2002), 93-108.
doi: 10.1142/S0219493702000327. |
[18] |
M. Patrão and L. A. B. San Martin, Semiflows on topological spaces: Chain transitivity and semigroups, J. Dynam. Differential Equations 19 (2007), 155-180.
doi: 10.1007/s10884-006-9032-3. |
[19] |
K. Twardowska, Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions, Dissertationes Math., (Rozprawy Mat.) 325 (1993), 54 pp. |
show all references
References:
[1] |
D. Applebaum, Lévy Processes and Stochastic Calculus, Cambridge University Press, 2004.
doi: 10.1017/CBO9780511755323. |
[2] |
J. M. Bismut, Mécanique Aléatoire, Lecture Notes in Math., 866. Springer-Verlag, Berlin-New York, 1981. |
[3] |
P. J. Catuogno, F. B. da Silva and P. R. Ruffino, Decomposition of stochastic flows with automorphism of subbundles component, Stochastics and Dynamics, 12 (2012), 1150013, 15 pp.
doi: 10.1142/S0219493712003705. |
[4] |
P. J. Catuogno, F. B. da Silva and P. R. Ruffino, Decomposition of stochastic flows in manifolds with complementary distributions, Stochastics and Dynamics, 13 (2013), 1350009, 12 pp.
doi: 10.1142/S0219493713500093. |
[5] |
F. Colonius and W. Kliemann, The Dynamics of Control, Systems and Control: Foundations and Applications. Birkhäuser Boston, Inc., Boston, MA, 2000.
doi: 10.1007/978-1-4612-1350-5. |
[6] |
F. Colonius and P. R. Ruffino, Nonlinear Iwasawa decomposition of control flows, Discrete Continuous Dyn. Systems, (Serie A) 18 (2007), 339-354.
doi: 10.3934/dcds.2007.18.339. |
[7] |
I. G. Gargate and P. R. Ruffino, An averaging principle for diffusions in foliated spaces, The Annals of Probab., 44 (2016), 567-588.
doi: 10.1214/14-AOP982. |
[8] |
H. Kunita, Stochastic differential equations and stochastic flows of diffeomorphisms, in: École d'Eté de Probabilités de Saint-Flour XII - 1982, ed. P.L. Hennequin, Lecture Notes on Maths., Springer, 1097 (1984), 143-303.
doi: 10.1007/BFb0099433. |
[9] |
H. Kunita, Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, Cambridge, 1997. |
[10] |
X.-M. Li, An averaging principle for a completely integrable stochastic Hamiltonian system, Nonlinearity, 21 (2008), 803-822.
doi: 10.1088/0951-7715/21/4/008. |
[11] |
T. Kurtz, E. Pardoux and P. Protter, Stratonovich stochastic differential equations driven by general semimartingales, Annales de l'I.H.P., section B, 31 (1995), 351-377. |
[12] |
M. Liao, Decomposition of stochastic flows and Lyapunov exponents, Probab. Theory Rel. Fields, 117 (2000), 589-607.
doi: 10.1007/PL00008736. |
[13] |
J. Milnor, Remarks on infinite dimensional lie groups, In: Relativity, Groups and Topology II, Les Houches Session XL, 1983, North Holland, Amsterdam, 1984, 1007-1057. |
[14] |
K.-H. Neeb, Infinite Dimesional Lie Groups, Monastir Summer Schoool, 2009. Available from hal.archives-ouvertes.fr/docs/00/39/.../CoursKarl-HermannNeeb.pdf. |
[15] |
H. Omori, Infinite Dimensional Lie Groups, Translations of Math Monographs 158, AMS, 1997. |
[16] |
L. Morgado and P. Ruffino, Extension of time for decomposition of stochastic flows in spaces with complementary foliations, Electron. Comm. Probab., 20 (2015), 9pp.
doi: 10.1214/ECP.v20-3762. |
[17] |
P. Ruffino, Decomposition of stochastic flow and rotation matrix, Stochastics and Dynamics, 2 (2002), 93-108.
doi: 10.1142/S0219493702000327. |
[18] |
M. Patrão and L. A. B. San Martin, Semiflows on topological spaces: Chain transitivity and semigroups, J. Dynam. Differential Equations 19 (2007), 155-180.
doi: 10.1007/s10884-006-9032-3. |
[19] |
K. Twardowska, Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions, Dissertationes Math., (Rozprawy Mat.) 325 (1993), 54 pp. |
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