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Stochastic differential equations

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Placeholder. A time-indexed, causal, measure-valued stochastic process As seen in state filters, optimal control, financial mathematics etc.


Applebaum, David, and Markus Riedle. 2010. “Cylindrical Levy Processes in Banach Spaces.” Proceedings of the London Mathematical Society 101 (3): 697–726.

Baudoin, Fabrice. 2014. Diffusion Processes and Stochastic Calculus. EMS Textbooks in Mathematics. Zurich, Switzerland: European Mathematical Society.

Baudoin, Fabrice, and Alice Vatamanelu. n.d. “Stochastic Calculus,” 114.

Bertoin, Jean, Marc Yor, and others. 2001. “On Subordinators, Self-Similar Markov Processes and Some Factorizations of the Exponential Variable.” Electron. Comm. Probab 6 (95): 106.

Coulaud, Benjamin, and Frédéric JP Richard. 2018. “A Consistent Framework for a Statistical Analysis of Surfaces Based on Generalized Stochastic Processes.”

Hairer, Martin. 2009. “An Introduction to Stochastic PDEs.”

Karczewska, Anna. 2007. “Convolution Type Stochastic Volterra Equations,” December.

Lindgren, Finn, Håvard Rue, and Johan Lindström. 2011. “An Explicit Link Between Gaussian Fields and Gaussian Markov Random Fields: The Stochastic Partial Differential Equation Approach.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 73 (4): 423–98.

Matheron, G. 1973. “The Intrinsic Random Functions and Their Applications.” Advances in Applied Probability 5 (3): 439–68.

Meidan, R. 1980. “On the Connection Between Ordinary and Generalized Stochastic Processes.” Journal of Mathematical Analysis and Applications 76 (1): 124–33.

Mikosch, Thomas, and Rimas Norvaiša. 2000. “Stochastic Integral Equations Without Probability.” Bernoulli 6 (3): 401–34.

Mohammed, Salah-Eldin A., and Michael K. R. Scheutzow. 1997. “Lyapunov Exponents of Linear Stochastic Functional-Differential Equations. II. Examples and Case Studies.” The Annals of Probability 25 (3): 1210–40.

Papaspiliopoulos, Omiros, Yvo Pokern, Gareth O. Roberts, and Andrew M. Stuart. 2012. “Nonparametric Estimation of Diffusions: A Differential Equations Approach.” Biometrika 99 (3): 511–31.

Rackauckas, Christopher, Yingbo Ma, Vaibhav Dixit, Xingjian Guo, Mike Innes, Jarrett Revels, Joakim Nyberg, and Vijay Ivaturi. 2018. “A Comparison of Automatic Differentiation and Continuous Sensitivity Analysis for Derivatives of Differential Equation Solutions,” December.

Särkkä, Simo, and Arno Solin. 2019. Applied Stochastic Differential Equations. Institute of Mathematical Statistics Textbooks 10. Cambridge ; New York, NY: Cambridge University Press.

Yaglom, A. M. 1987. Correlation Theory of Stationary and Related Random Functions: Supplementary Notes and References. New York, NY: Springer Science & Business Media.