Backward stochastic differential equations

September 19, 2019 — June 22, 2021

dynamical systems
Lévy processes
probability
SDEs
signal processing
stochastic processes
time series
Figure 1

Placeholder. Keywords: nonlinear Feynman-Kac. Some kind of connection to optimal control?

1 References

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Bao, Cao, Meir, et al. 2016. “A First Order Scheme for Backward Doubly Stochastic Differential Equations.” SIAM/ASA Journal on Uncertainty Quantification.
Carbone, Ferrario, and Santacroce. 2008. “Backward Stochastic Differential Equations Driven By Càdlàg Martingales.” Theory of Probability and Its Applications.
El Karoui, Nicole, Hamadene, and Matoussi. 2008. “Backward Stochastic Differential Equations and Applications.” Indifference Pricing : Theory and Applications.
El Karoui, N., Peng, and Quenez. 1997. “Backward Stochastic Differential Equations in Finance.” Mathematical Finance.
Gobet, Lemor, and Warin. 2005. “A Regression-Based Monte Carlo Method to Solve Backward Stochastic Differential Equations.” The Annals of Applied Probability.
Kim. 2021. “Arbitrage-Free Valuation in Nonlinear Financial Models.”
Kushner, and DiMasi. 1978. “Approximations for Functionals and Optimal Control Problems on Jump Diffusion Processes.” Journal of Mathematical Analysis and Applications.
Pardoux. 1995. “Backward Stochastic Differential Equations and Applications.” In Proceedings of the International Congress of Mathematicians.
Peng. 2011. “Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications.” In Proceedings of the International Congress of Mathematicians 2010 (ICM 2010).
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Perkowski. 2011. “Backward Stochastic Differential Equations: An Introduction.”
Pham. 2015. “Feynman-Kac Representation of Fully Nonlinear PDEs and Applications.” Acta Mathematica Vietnamica.
Şimşekli, Sener, Deligiannidis, et al. 2020. “Hausdorff Dimension, Stochastic Differential Equations, and Generalization in Neural Networks.” CoRR.
Wolpert, and Brown. 2021. “Markov Infinitely-Divisible Stationary Time-Reversible Integer-Valued Processes.” arXiv:2105.14591 [Math].