American Institute of Mathematical Sciences

September  2018, 17(5): 2125-2133. doi: 10.3934/cpaa.2018100

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

* Corresponding author

Received  October 2017 Revised  January 2018 Published  April 2018

Fund Project: The third author is supported by NNSFC (11771326, 11431014).

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.

Citation: Xing Huang, Chang Liu, Feng-Yu Wang. Order preservation for path-distribution dependent SDEs. Communications on Pure & Applied Analysis, 2018, 17 (5) : 2125-2133. doi: 10.3934/cpaa.2018100
References:

show all references

References:
 [1] Xing Huang, Michael Röckner, Feng-Yu Wang. Nonlinear Fokker–Planck equations for probability measures on path space and path-distribution dependent SDEs. Discrete & Continuous Dynamical Systems - A, 2019, 39 (6) : 3017-3035. doi: 10.3934/dcds.2019125 [2] Biswajit Sarkar, Buddhadev Mandal, Sumon Sarkar. Preservation of deteriorating seasonal products with stock-dependent consumption rate and shortages. Journal of Industrial & Management Optimization, 2017, 13 (1) : 187-206. doi: 10.3934/jimo.2016011 [3] Muhammad Waqas Iqbal, Biswajit Sarkar. Application of preservation technology for lifetime dependent products in an integrated production system. Journal of Industrial & Management Optimization, 2020, 16 (1) : 141-167. doi: 10.3934/jimo.2018144 [4] Pieter Moree. On the distribution of the order over residue classes. Electronic Research Announcements, 2006, 12: 121-128. [5] 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 [6] Roland Pulch. Stability preservation in Galerkin-type projection-based model order reduction. Numerical Algebra, Control & Optimization, 2019, 9 (1) : 23-44. doi: 10.3934/naco.2019003 [7] Shanjian Tang, Fu Zhang. Path-dependent optimal stochastic control and viscosity solution of associated Bellman equations. Discrete & Continuous Dynamical Systems - A, 2015, 35 (11) : 5521-5553. doi: 10.3934/dcds.2015.35.5521 [8] Jiann-Sheng Jiang, Kung-Hwang Kuo, Chi-Kun Lin. Homogenization of second order equation with spatial dependent coefficient. Discrete & Continuous Dynamical Systems - A, 2005, 12 (2) : 303-313. doi: 10.3934/dcds.2005.12.303 [9] Gábor Kiss, Bernd Krauskopf. Stability implications of delay distribution for first-order and second-order systems. Discrete & Continuous Dynamical Systems - B, 2010, 13 (2) : 327-345. doi: 10.3934/dcdsb.2010.13.327 [10] Ummugul Bulut, Edward J. Allen. Derivation of SDES for a macroevolutionary process. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1777-1792. doi: 10.3934/dcdsb.2013.18.1777 [11] A. V. Babin. Preservation of spatial patterns by a hyperbolic equation. Discrete & Continuous Dynamical Systems - A, 2004, 10 (1&2) : 1-19. doi: 10.3934/dcds.2004.10.1 [12] Martin Frank, Armin Fügenschuh, Michael Herty, Lars Schewe. The coolest path problem. Networks & Heterogeneous Media, 2010, 5 (1) : 143-162. doi: 10.3934/nhm.2010.5.143 [13] Haiyang Wang, Jianfeng Zhang. Forward backward SDEs in weak formulation. Mathematical Control & Related Fields, 2018, 8 (3&4) : 1021-1049. doi: 10.3934/mcrf.2018044 [14] José M. Arrieta, Esperanza Santamaría. Estimates on the distance of inertial manifolds. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 3921-3944. doi: 10.3934/dcds.2014.34.3921 [15] Liliana Trejo-Valencia, Edgardo Ugalde. Projective distance and $g$-measures. Discrete & Continuous Dynamical Systems - B, 2015, 20 (10) : 3565-3579. doi: 10.3934/dcdsb.2015.20.3565 [16] Kevin Ford. The distribution of totients. Electronic Research Announcements, 1998, 4: 27-34. [17] Hong-Kun Zhang. Free path of billiards with flat points. Discrete & Continuous Dynamical Systems - A, 2012, 32 (12) : 4445-4466. doi: 10.3934/dcds.2012.32.4445 [18] Matthias Gerdts, René Henrion, Dietmar Hömberg, Chantal Landry. Path planning and collision avoidance for robots. Numerical Algebra, Control & Optimization, 2012, 2 (3) : 437-463. doi: 10.3934/naco.2012.2.437 [19] Helge Dietert, Josephine Evans, Thomas Holding. Contraction in the Wasserstein metric for the kinetic Fokker-Planck equation on the torus. Kinetic & Related Models, 2018, 11 (6) : 1427-1441. doi: 10.3934/krm.2018056 [20] Karoline Disser, Matthias Liero. On gradient structures for Markov chains and the passage to Wasserstein gradient flows. Networks & Heterogeneous Media, 2015, 10 (2) : 233-253. doi: 10.3934/nhm.2015.10.233

2018 Impact Factor: 0.925