-
Previous Article
A note concerning a property of symplectic matrices
- CPAA Home
- This Issue
-
Next Article
Concentration phenomena for critical fractional Schrödinger systems
Order preservation for path-distribution dependent SDEs
1. | Center for Applied Mathematics, Tianjin University, Tianjin 300072, China |
2. | School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China |
3. | Department of Mathematics, Swansea University, Singleton Park, SA2 8PP, United Kingdom |
Sufficient and necessary conditions are presented for the order preservation of path-distribution dependent SDEs. Differently from the corresponding study of distribution independent SDEs, to investigate the necessity of order preservation for the present model we need to construct a family of probability spaces in terms of the ordered pair of initial distributions.
References:
[1] |
J. Bao and C. Yuan,
Comparison theorem for stochastic differential delay equations with jumps, Acta Appl. Math., 116 (2011), 119-132.
|
[2] |
M.-F. Chen and F.-Y. Wang,
On order-preservation and positive correlations for multidimensional diffusion processes, Prob. Theory. Relat. Fields, 95 (1993), 421-428.
|
[3] |
L. Gal'cuk and M. Davis,
A note on a comparison theorem for equations with different diffusions, Stochastics, 6 (1982), 147-149.
|
[4] |
X. Huang, M. Röckner and F.-Y. Wang, Nonlinear Fokker–Planck equations for probability
measures on path space and path-distribution dependent SDEs, preprint, arXiv: 1709.00556. |
[5] |
X. Huang and F.-Y. Wang,
Order-preservation for multidimensional stochastic functional differential equations with jumps, J. Evol. Equat., 14 (2014), 445-460.
|
[6] |
N. Ikeda and S. Watanabe,
A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math., 14 (1977), 619-633.
|
[7] |
T. Kamae, U. Krengel and G. L. O'Brien,
Stochastic inequalities on partially ordered spaces, Ann. Probab., 5 (1977), 899-912.
|
[8] |
X. Mao,
A note on comparison theorems for stochastic differential equations with respect to semimartingales, Stochastics, 37 (1991), 49-59.
|
[9] |
G. L. O'Brien,
A new comparison theorem for solution of stochastic differential equations, Stochastics, 3 (1980), 245-249.
|
[10] |
S. Peng and Z. Yang,
Anticipated backward stochastic differential equations, Ann. Probab., 37 (2009), 877-902.
|
[11] |
S. Peng and X. Zhu,
Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations, Stochastic Process. Appl., 116 (2006), 370-380.
|
[12] |
F.-Y. Wang,
The stochastic order and critical phenomena for superprocesses, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 9 (2006), 107-128.
|
[13] |
F.-Y. Wang,
Distribution-dependent SDEs for Landau type equations, Stoch. Proc. Appl., 128 (2018), 595-621.
|
[14] |
J.-M. Wang,
Stochastic comparison for Lévy-type processes, J. Theor. Probab., 26 (2013), 997-1019.
|
[15] |
Z. Yang, X. Mao and C. Yuan,
Comparison theorem of one-dimensional stochastic hybrid systems, Systems Control Lett., 57 (2008), 56-63.
|
[16] |
X. Zhu,
On the comparison theorem for multi-dimensional stochastic differential equations with jumps (in Chinese), Sci. Sin. Math., 42 (2012), 303-311.
|
show all references
References:
[1] |
J. Bao and C. Yuan,
Comparison theorem for stochastic differential delay equations with jumps, Acta Appl. Math., 116 (2011), 119-132.
|
[2] |
M.-F. Chen and F.-Y. Wang,
On order-preservation and positive correlations for multidimensional diffusion processes, Prob. Theory. Relat. Fields, 95 (1993), 421-428.
|
[3] |
L. Gal'cuk and M. Davis,
A note on a comparison theorem for equations with different diffusions, Stochastics, 6 (1982), 147-149.
|
[4] |
X. Huang, M. Röckner and F.-Y. Wang, Nonlinear Fokker–Planck equations for probability
measures on path space and path-distribution dependent SDEs, preprint, arXiv: 1709.00556. |
[5] |
X. Huang and F.-Y. Wang,
Order-preservation for multidimensional stochastic functional differential equations with jumps, J. Evol. Equat., 14 (2014), 445-460.
|
[6] |
N. Ikeda and S. Watanabe,
A comparison theorem for solutions of stochastic differential equations and its applications, Osaka J. Math., 14 (1977), 619-633.
|
[7] |
T. Kamae, U. Krengel and G. L. O'Brien,
Stochastic inequalities on partially ordered spaces, Ann. Probab., 5 (1977), 899-912.
|
[8] |
X. Mao,
A note on comparison theorems for stochastic differential equations with respect to semimartingales, Stochastics, 37 (1991), 49-59.
|
[9] |
G. L. O'Brien,
A new comparison theorem for solution of stochastic differential equations, Stochastics, 3 (1980), 245-249.
|
[10] |
S. Peng and Z. Yang,
Anticipated backward stochastic differential equations, Ann. Probab., 37 (2009), 877-902.
|
[11] |
S. Peng and X. Zhu,
Necessary and sufficient condition for comparison theorem of 1-dimensional stochastic differential equations, Stochastic Process. Appl., 116 (2006), 370-380.
|
[12] |
F.-Y. Wang,
The stochastic order and critical phenomena for superprocesses, Infin. Dimens. Anal. Quantum Probab. Relat. Top., 9 (2006), 107-128.
|
[13] |
F.-Y. Wang,
Distribution-dependent SDEs for Landau type equations, Stoch. Proc. Appl., 128 (2018), 595-621.
|
[14] |
J.-M. Wang,
Stochastic comparison for Lévy-type processes, J. Theor. Probab., 26 (2013), 997-1019.
|
[15] |
Z. Yang, X. Mao and C. Yuan,
Comparison theorem of one-dimensional stochastic hybrid systems, Systems Control Lett., 57 (2008), 56-63.
|
[16] |
X. Zhu,
On the comparison theorem for multi-dimensional stochastic differential equations with jumps (in Chinese), Sci. Sin. Math., 42 (2012), 303-311.
|
[1] |
Xing Huang, Michael Röckner, Feng-Yu Wang. Nonlinear Fokker–Planck equations for probability measures on path space and path-distribution dependent SDEs. Discrete and Continuous Dynamical Systems, 2019, 39 (6) : 3017-3035. doi: 10.3934/dcds.2019125 |
[2] |
Xing Huang, Feng-Yu Wang. Mckean-Vlasov sdes with drifts discontinuous under wasserstein distance. Discrete and Continuous Dynamical Systems, 2021, 41 (4) : 1667-1679. doi: 10.3934/dcds.2020336 |
[3] |
Jianhai Bao, Feng-Yu Wang, Chenggui Yuan. Limit theorems for additive functionals of path-dependent SDEs. Discrete and Continuous Dynamical Systems, 2020, 40 (9) : 5173-5188. doi: 10.3934/dcds.2020224 |
[4] |
Kaitong Hu, Zhenjie Ren, Nizar Touzi. On path-dependent multidimensional forward-backward SDEs. Numerical Algebra, Control and Optimization, 2022 doi: 10.3934/naco.2022010 |
[5] |
Yulin Song. Density functions of distribution dependent SDEs driven by Lévy noises. Communications on Pure and Applied Analysis, 2021, 20 (6) : 2399-2419. doi: 10.3934/cpaa.2021087 |
[6] |
Panpan Ren, Shen Wang. Moderate deviation principles for unbounded additive functionals of distribution dependent SDEs. Communications on Pure and Applied Analysis, 2021, 20 (9) : 3129-3142. doi: 10.3934/cpaa.2021099 |
[7] |
Xing Huang, Yulin Song, Feng-Yu Wang. Bismut formula for intrinsic/Lions derivatives of distribution dependent SDEs with singular coefficients. Discrete and Continuous Dynamical Systems, 2022 doi: 10.3934/dcds.2022065 |
[8] |
Qing Ma, Yanjun Wang. Distributionally robust chance constrained svm model with $\ell_2$-Wasserstein distance. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021212 |
[9] |
Muhammad Waqas Iqbal, Biswajit Sarkar. Application of preservation technology for lifetime dependent products in an integrated production system. Journal of Industrial and Management Optimization, 2020, 16 (1) : 141-167. doi: 10.3934/jimo.2018144 |
[10] |
Biswajit Sarkar, Buddhadev Mandal, Sumon Sarkar. Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages. Journal of Industrial and Management Optimization, 2017, 13 (1) : 187-206. doi: 10.3934/jimo.2016011 |
[11] |
Pieter Moree. On the distribution of the order over residue classes. Electronic Research Announcements, 2006, 12: 121-128. |
[12] |
Xingchun Wang. Pricing path-dependent options under the Hawkes jump diffusion process. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022024 |
[13] |
Carlos Munuera, Fernando Torres. A note on the order bound on the minimum distance of AG codes and acute semigroups. Advances in Mathematics of Communications, 2008, 2 (2) : 175-181. doi: 10.3934/amc.2008.2.175 |
[14] |
Roland Pulch. Stability preservation in Galerkin-type projection-based model order reduction. Numerical Algebra, Control and Optimization, 2019, 9 (1) : 23-44. doi: 10.3934/naco.2019003 |
[15] |
Yanyan Hu, Fubao Xi, Min Zhu. Least squares estimation for distribution-dependent stochastic differential delay equations. Communications on Pure and Applied Analysis, 2022, 21 (4) : 1505-1536. doi: 10.3934/cpaa.2022027 |
[16] |
Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete and Continuous Dynamical Systems, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 |
[17] |
Ludger Overbeck, Jasmin A. L. Röder. Path-dependent backward stochastic Volterra integral equations with jumps, differentiability and duality principle. Probability, Uncertainty and Quantitative Risk, 2018, 3 (0) : 4-. doi: 10.1186/s41546-018-0030-2 |
[18] |
Jiann-Sheng Jiang, Kung-Hwang Kuo, Chi-Kun Lin. Homogenization of second order equation with spatial dependent coefficient. Discrete and Continuous Dynamical Systems, 2005, 12 (2) : 303-313. doi: 10.3934/dcds.2005.12.303 |
[19] |
Gábor Kiss, Bernd Krauskopf. Stability implications of delay distribution for first-order and second-order systems. Discrete and Continuous Dynamical Systems - B, 2010, 13 (2) : 327-345. doi: 10.3934/dcdsb.2010.13.327 |
[20] |
A. V. Babin. Preservation of spatial patterns by a hyperbolic equation. Discrete and Continuous Dynamical Systems, 2004, 10 (1&2) : 1-19. doi: 10.3934/dcds.2004.10.1 |
2020 Impact Factor: 1.916
Tools
Metrics
Other articles
by authors
[Back to Top]