Approximate McKean–Vlasov representations for a class of SPDEs

By D. Crisan, Jie-Yu Xiong. 2005

111 citations recorded by the source corpus.

The solution of a class of linear stochastic partial differential equations is approximated using Clark's robust representation approach. The ensuing approximations are shown to coincide with the time marginals of solutions of a certain McKean–Vlasov type equation. We prove existence and uniqueness of the solution of the McKean–Vlasov equation.

Subfields: Artificial Intelligence, Finance, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c986a8de08c367ad157a75f12c3eb4e5e9382012

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jiongmin Yong
2. D. Crisan
3. Federico Castanedo
4. Peter E. Kloeden
5. Arnulf Jentzen

In Finance

1. D. Crisan
2. K. Manolarakis
3. Jiongmin Yong
4. Yuliya S. Mishura
5. Nizar Touzi
6. Gonçalo dos Reis
7. Alexander Yur'evich Veretennikov
8. Jianfeng Zhang

In Statistical and Nonlinear Physics

1. Jiongmin Yong
2. Gonçalo dos Reis
3. Nizar Touzi
4. Alexander Yur'evich Veretennikov

Citations in the corpus

• A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations (2011, background): “In recent years, related topics and problems have attracted more and more researchers’ attentions, see, for examples, Veretennikov [32], Huang–Malhamé– Caines [17], Mahmudov–McKibben [23], Buckdahn-Djehiche-Li-Peng [8], Buckdahn-Li-Peng [9], Borkar– Kumar [6], Crisan–Xiong [12], Kotelenez–Kurtz [20”
• On the Monte Carlo simulation of BSDEs: An improvement on the Malliavin weights (2010, background): “Finding a suitable way to deal with the instability of the approximations of Riesz integrals remains a hard problem (see [12] for another application of Riesz integral in a different context).”
• Linear Quadratic Optimal Control Problems for Mean-Field Backward Stochastic Differential Equations (2016, unknown): “Typical representatives include, but not limited to, McKean [27], Dawson [15], Chan [12], Buckdahn–Djehiche–Li–Peng [6], Buckdahn–Li–Peng [7], Borkar–Kumar [5], Crisan–Xiong [14], Andersson–Djehiche [2], Buckdahn–Djehiche–Li [8], MeyerBrandis–Oksendal–Zhou [28], Yong [35,36], Huang–Li–Yong [20], Li–”
• Freidlin–Wentzell LDP in path space for McKean–Vlasov equations and the functional iterated logarithm law (2017, background): “For applications, see [11] about social interactions or [13] about the stochastic partial differential equations.”
• Existence and uniqueness theorems for solutions of McKean–Vlasov stochastic equations (2016, background): “McKean–Vlasov’s equations, being clearly more involved than Itô’s SDEs, arise in multi-agent systems (see [2, 3]), as well as in some other areas of high interest such as filtering (see [5]).”
• A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon (2012, unknown): “For the relevant works of recent years, see, for examples, Veretennikov [34], Huang– Malhamé–Caines [22], Buckdahn-Djehiche-Li-Peng [12], Buckdahn-Li-Peng [13], Borkar–Kumar [9], Crisan– Xiong [16], Kotelenez–Kurtz [25], and so on.”