Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs

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Cheridito, Patrick, et al. “Second‐order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs”. Communications on Pure and Applied Mathematics, vol. 60, no. 7, 2006, pp. 1081-10, https://doi.org/10.1002/cpa.20168.
Cheridito, P., Soner, H. M., Touzi, N., & Victoir, N. (2006). Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs. Communications on Pure and Applied Mathematics, 60(7), 1081-1110. https://doi.org/10.1002/cpa.20168
Cheridito, Patrick, H. Mete Soner, Nizar Touzi, and Nicolas Victoir. “Second‐order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs”. Communications on Pure and Applied Mathematics 60, no. 7 (2006): 1081-1110. https://doi.org/10.1002/cpa.20168.
Cheridito P, Soner HM, Touzi N, Victoir N. Second‐order backward stochastic differential equations and fully nonlinear parabolic PDEs. Communications on Pure and Applied Mathematics. 2006;60(7):1081-110.
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Necessary optimality conditions in problems of the control of stochastic differential equations 1979
Monte Carlo methods in financial engineering 2004
Statistics of random processes. I. General theory 2001
Forward‐backward stochastic differential equations and their applications 1999
Citations
Title Journal Journal Categories Citations Publication Date
Numerical approximation based on deep convolutional neural network for high‐dimensional fully nonlinear merged PDEs and 2BSDEs

 Mathematical Methods in the Applied Sciences
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 2024
Optimal stopping of BSDEs with constrained jumps and related zero-sum games Stochastic Processes and their Applications
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 2024
The One Step Malliavin scheme: new discretization of BSDEs implemented with deep learning regressions

 IMA Journal of Numerical Analysis
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Citations Analysis
Category Category Repetition
Science: Mathematics99
Science: Mathematics: Probabilities. Mathematical statistics51
Technology: Technology (General): Industrial engineering. Management engineering: Applied mathematics. Quantitative methods38
Social Sciences: Finance17
Social Sciences: Statistics14
Social Sciences: Economic theory. Demography: Economics as a science14
Social Sciences: Commerce: Business14
Technology: Engineering (General). Civil engineering (General)10
Technology: Mechanical engineering and machinery8
Science: Mathematics: Instruments and machines: Electronic computers. Computer science5
Science: Physics5
Technology: Manufactures: Production management. Operations management2
Technology: Electrical engineering. Electronics. Nuclear engineering: Electronics1
Technology: Engineering (General). Civil engineering (General): Mechanics of engineering. Applied mechanics1
The category Science: Mathematics 99 is the most commonly referenced area in studies that cite this article. The first research to cite this article was titled Classical and Variational Differentiability of BSDEs with Quadratic Growth and was published in 2007. The most recent citation comes from a 2024 study titled Optimal stopping of BSDEs with constrained jumps and related zero-sum games. This article reached its peak citation in 2020, with 12 citations. It has been cited in 49 different journals, 6% of which are open access. Among related journals, the SSRN Electronic Journal cited this research the most, with 20 citations. The chart below illustrates the annual citation trends for this article.
Citations used this article by year