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Journal articles on the topic 'McKean Vlasov equations'

Author: Grafiati

Published: 4 June 2021

Last updated: 3 February 2022

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1

Dawson, Donald, and Jean Vaillancourt. "Stochastic McKean-Vlasov equations." Nonlinear Differential Equations and Applications NoDEA 2, no. 2 (1995): 199–229. http://dx.doi.org/10.1007/bf01295311.

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2

Wang, Weifeng, Lei Yan, Junhao Hu, and Zhongkai Guo. "An Averaging Principle for Mckean–Vlasov-Type Caputo Fractional Stochastic Differential Equations." Journal of Mathematics 2021 (July 16, 2021): 1–11. http://dx.doi.org/10.1155/2021/8742330.

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In this paper, we want to establish an averaging principle for Mckean–Vlasov-type Caputo fractional stochastic differential equations with Brownian motion. Compared with the classic averaging condition for stochastic differential equation, we propose a new averaging condition and obtain the averaging convergence results for Mckean–Vlasov-type Caputo fractional stochastic differential equations.

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3

Qiao, Huijie, and Jiang-Lun Wu. "Path independence of the additive functionals for McKean–Vlasov stochastic differential equations with jumps." Infinite Dimensional Analysis, Quantum Probability and Related Topics 24, no. 01 (2021): 2150006. http://dx.doi.org/10.1142/s0219025721500065.

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In this paper, the path independent property of additive functionals of McKean–Vlasov stochastic differential equations with jumps is characterized by nonlinear partial integro-differential equations involving [Formula: see text]-derivatives with respect to probability measures introduced by Lions. Our result extends the recent work16 by Ren and Wang where their concerned McKean–Vlasov stochastic differential equations are driven by Brownian motions.

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4

Bao, Jianhai, Christoph Reisinger, Panpan Ren, and Wolfgang Stockinger. "First-order convergence of Milstein schemes for McKean–Vlasov equations and interacting particle systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (2021): 20200258. http://dx.doi.org/10.1098/rspa.2020.0258.

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In this paper, we derive fully implementable first-order time-stepping schemes for McKean–Vlasov stochastic differential equations, allowing for a drift term with super-linear growth in the state component. We propose Milstein schemes for a time-discretized interacting particle system associated with the McKean–Vlasov equation and prove strong convergence of order 1 and moment stability, taming the drift if only a one-sided Lipschitz condition holds. To derive our main results on strong convergence rates, we make use of calculus on the space of probability measures with finite second-order mom

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5

Mahmudov, N. I., and M. A. McKibben. "Abstract Second-Order Damped McKean-Vlasov Stochastic Evolution Equations." Stochastic Analysis and Applications 24, no. 2 (2006): 303–28. http://dx.doi.org/10.1080/07362990500522247.

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6

Bahlali, Khaled, Mohamed Amine Mezerdi, and Brahim Mezerdi. "Stability of McKean–Vlasov stochastic differential equations and applications." Stochastics and Dynamics 20, no. 01 (2019): 2050007. http://dx.doi.org/10.1142/s0219493720500070.

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We consider McKean–Vlasov stochastic differential equations (MVSDEs), which are SDEs where the drift and diffusion coefficients depend not only on the state of the unknown process but also on its probability distribution. This type of SDEs was studied in statistical physics and represents the natural setting for stochastic mean-field games. We will first discuss questions of existence and uniqueness of solutions under an Osgood type condition improving the well-known Lipschitz case. Then, we derive various stability properties with respect to initial data, coefficients and driving processes, g

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7

Lv, Li, Yanjie Zhang, and Zibo Wang. "Information upper bound for McKean–Vlasov stochastic differential equations." Chaos: An Interdisciplinary Journal of Nonlinear Science 31, no. 5 (2021): 051103. http://dx.doi.org/10.1063/5.0049874.

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8

Mehri, Sima, and Wilhelm Stannat. "Weak solutions to Vlasov–McKean equations under Lyapunov-type conditions." Stochastics and Dynamics 19, no. 06 (2019): 1950042. http://dx.doi.org/10.1142/s0219493719500424.

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We present a Lyapunov-type approach to the problem of existence and uniqueness of general law-dependent stochastic differential equations. In the existing literature, most results concerning existence and uniqueness are obtained under regularity assumptions of the coefficients with respect to the Wasserstein distance. Some existence and uniqueness results for irregular coefficients have been obtained by considering the total variation distance. Here, we extend this approach to the control of the solution in some weighted total variation distance, that allows us now to derive a rather general w

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9

Schlichting, André, Vaios Laschos, Max Fathi, and Matthias Erbar. "Gradient flow structure for McKean-Vlasov equations on discrete spaces." Discrete and Continuous Dynamical Systems 36, no. 12 (2016): 6799–833. http://dx.doi.org/10.3934/dcds.2016096.

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10

Govindan, T. E., and N. U. Ahmed. "On Yosida Approximations of McKean–Vlasov Type Stochastic Evolution Equations." Stochastic Analysis and Applications 33, no. 3 (2015): 383–98. http://dx.doi.org/10.1080/07362994.2014.993766.

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11

Scheutzow, Michael. "Uniqueness and non-uniqueness of solutions of Vlasov-McKean equations." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 43, no. 2 (1987): 246–56. http://dx.doi.org/10.1017/s1446788700029384.

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AbstractWe study the equation dY(t)/dt = f(Y(t), Eh(Y(t))) for random initial conditions, where E denotes the expected value. It turns out that in contrast to the deterministic case local Lipschitz continuity of f and h are not sufficient to ensure uniqueness of the solutions. Finally we also state some sufficient conditions for uniqueness.

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12

Carmona, René, and François Delarue. "Forward–backward stochastic differential equations and controlled McKean–Vlasov dynamics." Annals of Probability 43, no. 5 (2015): 2647–700. http://dx.doi.org/10.1214/14-aop946.

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13

Belomestny, Denis, and John Schoenmakers. "Projected Particle Methods for Solving McKean--Vlasov Stochastic Differential Equations." SIAM Journal on Numerical Analysis 56, no. 6 (2018): 3169–95. http://dx.doi.org/10.1137/17m1111024.

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14

Şen, Nevroz, and Peter E. Caines. "Nonlinear Filtering Theory for McKean--Vlasov Type Stochastic Differential Equations." SIAM Journal on Control and Optimization 54, no. 1 (2016): 153–74. http://dx.doi.org/10.1137/15m1013304.

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15

Agram, Nacira. "Stochastic optimal control of McKean–Vlasov equations with anticipating law." Afrika Matematika 30, no. 5-6 (2019): 879–901. http://dx.doi.org/10.1007/s13370-019-00689-w.

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16

Mezerdi, Mohamed Amine. "Compactification in optimal control of McKean‐Vlasov stochastic differential equations." Optimal Control Applications and Methods 42, no. 4 (2021): 1161–77. http://dx.doi.org/10.1002/oca.2721.

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17

Ding, Xiaojie, and Huijie Qiao. "Stability for Stochastic McKean--Vlasov Equations with Non-Lipschitz Coefficients." SIAM Journal on Control and Optimization 59, no. 2 (2021): 887–905. http://dx.doi.org/10.1137/19m1289418.

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18

Tugaut, Julian. "Finiteness of entropy for granular media equations." Probability and Mathematical Statistics 39, no. 1 (2019): 75–84. http://dx.doi.org/10.19195/0208-4147.39.1.5.

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The current work deals with the granular media equation whose probabilistic interpretation is the McKean–Vlasov diffusion. It is well known that the Laplacian provides a regularization of the solution. Indeed, for any t > 0, the solution is absolutely continuous with respect to the Lebesgue measure. It has also been proved that all the moments are bounded for positive t. However, the finiteness of the entropy of the solution is a new result which will be presented here.

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19

Keck, David N., and Mark A. McKibben. "Abstract semilinear stochastic Itó-Volterra integrodifferential equations." Journal of Applied Mathematics and Stochastic Analysis 2006 (July 4, 2006): 1–22. http://dx.doi.org/10.1155/jamsa/2006/45253.

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We consider a class of abstract semilinear stochastic Volterra integrodifferential equations in a real separable Hilbert space. The global existence and uniqueness of a mild solution, as well as a perturbation result, are established under the so-called Caratheodory growth conditions on the nonlinearities. An approximation result is then established, followed by an analogous result concerning a so-called McKean-Vlasov integrodifferential equation, and then a brief commentary on the extension of the main results to the time-dependent case. The paper ends with a discussion of some concrete examp

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20

Wu, Zhen, and Ruimin Xu. "Probabilistic interpretation for Sobolev solutions of McKean–Vlasov partial differential equations." Statistics & Probability Letters 145 (February 2019): 273–83. http://dx.doi.org/10.1016/j.spl.2018.10.001.

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21

Kotelenez, Peter M., and Thomas G. Kurtz. "Macroscopic limits for stochastic partial differential equations of McKean–Vlasov type." Probability Theory and Related Fields 146, no. 1-2 (2008): 189–222. http://dx.doi.org/10.1007/s00440-008-0188-0.

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22

Muthukumar, P., and P. Balasubramaniam. "Approximate controllability of second-order damped McKean–Vlasov stochastic evolution equations." Computers & Mathematics with Applications 60, no. 10 (2010): 2788–96. http://dx.doi.org/10.1016/j.camwa.2010.09.032.

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23

Mezerdi, Mohamed Amine, and Nabil Khelfallah. "Stability and prevalence of McKean–Vlasov stochastic differential equations with non-Lipschitz coefficients." Random Operators and Stochastic Equations 29, no. 1 (2021): 67–78. http://dx.doi.org/10.1515/rose-2021-2053.

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Abstract We consider various approximation properties for systems driven by a McKean–Vlasov stochastic differential equations (MVSDEs) with continuous coefficients, for which pathwise uniqueness holds. We prove that the solution of such equations is stable with respect to small perturbation of initial conditions, parameters and driving processes. Moreover, the unique strong solutions may be constructed by an effective approximation procedure. Finally, we show that the set of bounded uniformly continuous coefficients for which the corresponding MVSDE have a unique strong solution is a set of se

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24

Chaudru de Raynal, P. E. "Strong well posedness of McKean–Vlasov stochastic differential equations with Hölder drift." Stochastic Processes and their Applications 130, no. 1 (2020): 79–107. http://dx.doi.org/10.1016/j.spa.2019.01.006.

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25

Butkovsky, O. A. "On Ergodic Properties of Nonlinear Markov Chains and Stochastic McKean--Vlasov Equations." Theory of Probability & Its Applications 58, no. 4 (2014): 661–74. http://dx.doi.org/10.1137/s0040585x97986825.

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26

McKibben, Mark A. "GENERAL EXISTENCE RESULTS FOR ABSTRACT McKEAN-VLASOV STOCHASTIC EQUATIONS WITH VARIABLE DELAY." Far East Journal of Mathematical Sciences (FJMS) 99, no. 9 (2016): 1335–70. http://dx.doi.org/10.17654/ms099091335.

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27

Graham, Carl. "McKean-Vlasov Ito-Skorohod equations, and nonlinear diffusions with discrete jump sets." Stochastic Processes and their Applications 40, no. 1 (1992): 69–82. http://dx.doi.org/10.1016/0304-4149(92)90138-g.

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28

Barbu, Viorel, and Michael Röckner. "Solutions for nonlinear Fokker–Planck equations with measures as initial data and McKean-Vlasov equations." Journal of Functional Analysis 280, no. 7 (2021): 108926. http://dx.doi.org/10.1016/j.jfa.2021.108926.

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29

Chaudru de Raynal, P. E., and C. A. Garcia Trillos. "A cubature based algorithm to solve decoupled McKean–Vlasov forward–backward stochastic differential equations." Stochastic Processes and their Applications 125, no. 6 (2015): 2206–55. http://dx.doi.org/10.1016/j.spa.2014.11.018.

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30

Wu, Cong, and Jianfeng Zhang. "Viscosity solutions to parabolic master equations and McKean–Vlasov SDEs with closed-loop controls." Annals of Applied Probability 30, no. 2 (2020): 936–86. http://dx.doi.org/10.1214/19-aap1521.

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31

Liu, Wei, Liming Wu, and Chaoen Zhang. "Long-Time Behaviors of Mean-Field Interacting Particle Systems Related to McKean–Vlasov Equations." Communications in Mathematical Physics 387, no. 1 (2021): 179–214. http://dx.doi.org/10.1007/s00220-021-04198-5.

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32

Nüsken, Nikolas, Sebastian Reich, and Paul J. Rozdeba. "State and Parameter Estimation from Observed Signal Increments." Entropy 21, no. 5 (2019): 505. http://dx.doi.org/10.3390/e21050505.

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The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors are correlated and both states and parameters need to be identified. Such scenarios arise from noisy and partial observations of Lagrangian particles which move under a stochastic velocity field involving unknown parameters. We take an appropriate class of McKean–Vlasov equations as the starting point to derive ensemble Kalman–Bucy filter algorithms for com

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33

Kotelenez, Peter. "A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation." Probability Theory and Related Fields 102, no. 2 (1995): 159–88. http://dx.doi.org/10.1007/bf01213387.

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34

dos Reis, Gonçalo, William Salkeld, and Julian Tugaut. "Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law." Annals of Applied Probability 29, no. 3 (2019): 1487–540. http://dx.doi.org/10.1214/18-aap1416.

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35

Hafayed, Mokhtar, Shahlar Meherrem, Şaban Eren, and Deniz Hasan Guçoglu. "On optimal singular control problem for general Mckean-Vlasov differential equations: Necessary and sufficient optimality conditions." Optimal Control Applications and Methods 39, no. 3 (2018): 1202–19. http://dx.doi.org/10.1002/oca.2403.

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36

Coppini, Fabio, Helge Dietert, and Giambattista Giacomin. "A law of large numbers and large deviations for interacting diffusions on Erdős–Rényi graphs." Stochastics and Dynamics 20, no. 02 (2019): 2050010. http://dx.doi.org/10.1142/s0219493720500100.

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We consider a class of particle systems described by differential equations (both stochastic and deterministic), in which the interaction network is determined by the realization of an Erdős–Rényi graph with parameter [Formula: see text], where [Formula: see text] is the size of the graph (i.e. the number of particles). If [Formula: see text], the graph is the complete graph (mean field model) and it is well known that, under suitable hypotheses, the empirical measure converges as [Formula: see text] to the solution of a PDE: a McKean–Vlasov (or Fokker–Planck) equation in the stochastic case,

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37

Ahmed, N. U. "Optimal control of general McKean-Vlasov stochastic evolution equations on Hilbert spaces and necessary conditions of optimality." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 35, no. 2 (2015): 165. http://dx.doi.org/10.7151/dmdico.1171.

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38

Talay, Denis, and Olivier Vaillant. "A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations." Annals of Applied Probability 13, no. 1 (2003): 140–80. http://dx.doi.org/10.1214/aoap/1042765665.

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39

McKibben, Mark A., and Micah Webster. "A class of second-order McKean–Vlasov stochastic evolution equations driven by fractional Brownian motion and Poisson jumps." Computers & Mathematics with Applications 79, no. 2 (2020): 391–406. http://dx.doi.org/10.1016/j.camwa.2019.07.013.

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40

Angiuli, Andrea, Christy V. Graves, Houzhi Li, Jean-François Chassagneux, François Delarue, and René Carmona. "Cemracs 2017: numerical probabilistic approach to MFG." ESAIM: Proceedings and Surveys 65 (2019): 84–113. http://dx.doi.org/10.1051/proc/201965084.

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This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaki

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41

Ahmed, N. U. "A general class of McKean-Vlasov stochastic evolution equations driven by Brownian motion and L\`evy process and controlled by L\`evy measure." Discussiones Mathematicae. Differential Inclusions, Control and Optimization 36, no. 2 (2016): 181. http://dx.doi.org/10.7151/dmdico.1186.

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42

Kushner, Harold J. "Approximations of large trunk line systems under heavy traffic." Advances in Applied Probability 26, no. 04 (1994): 1063–94. http://dx.doi.org/10.1017/s0001867800026768.

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The paper deals with large trunk line systems of the type appearing in telephone networks. There are many nodes or input sources, each pair of which is connected by a trunk line containing many individual circuits. Traffic arriving at either end of a trunk line wishes to communicate to the node at the other end. If the direct route is full, a rerouting might be attempted via an alternative route containing several trunks and connecting the same endpoints. The basic questions concern whether to reroute, and if so how to choose the alternative path. If the network is ‘large’ and fully connected,

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43

Kushner, Harold J. "Approximations of large trunk line systems under heavy traffic." Advances in Applied Probability 26, no. 4 (1994): 1063–94. http://dx.doi.org/10.2307/1427905.

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The paper deals with large trunk line systems of the type appearing in telephone networks. There are many nodes or input sources, each pair of which is connected by a trunk line containing many individual circuits. Traffic arriving at either end of a trunk line wishes to communicate to the node at the other end. If the direct route is full, a rerouting might be attempted via an alternative route containing several trunks and connecting the same endpoints. The basic questions concern whether to reroute, and if so how to choose the alternative path. If the network is ‘large’ and fully connected,

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44

Hong, Wei, Shihu Li, and Wei Liu. "Large Deviation Principle for McKean–Vlasov Quasilinear Stochastic Evolution Equations." Applied Mathematics & Optimization, July 2, 2021. http://dx.doi.org/10.1007/s00245-021-09796-2.

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45

Bao, Jianhai, and Xing Huang. "Approximations of McKean–Vlasov Stochastic Differential Equations with Irregular Coefficients." Journal of Theoretical Probability, February 26, 2021. http://dx.doi.org/10.1007/s10959-021-01082-9.

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46

Mezerdi, Mohamed Amine. "On the convergence of carathéodory numerical scheme for Mckean-Vlasov equations." Stochastic Analysis and Applications, November 10, 2020, 1–15. http://dx.doi.org/10.1080/07362994.2020.1845206.

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47

Röckner, Michael, Xiaobin Sun, and Yingchao Xie. "Strong convergence order for slow–fast McKean–Vlasov stochastic differential equations." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 57, no. 1 (2021). http://dx.doi.org/10.1214/20-aihp1087.

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48

Mishura, Yuliya, and Alexander Veretennikov. "Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations." Theory of Probability and Mathematical Statistics, June 16, 2021, 1. http://dx.doi.org/10.1090/tpms/1135.

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49

Xu, Jie, Juanfang Liu, Jicheng Liu, and Yu Miao. "Strong Averaging Principle for Two-Time-Scale Stochastic McKean-Vlasov Equations." Applied Mathematics & Optimization, May 27, 2021. http://dx.doi.org/10.1007/s00245-021-09787-3.

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50

Lacker, Daniel. "On a strong form of propagation of chaos for McKean-Vlasov equations." Electronic Communications in Probability 23 (2018). http://dx.doi.org/10.1214/18-ecp150.

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