I am already using YUIMA package for estimating stochastic differential equations.
I am wondering which software/packages researchers use for estimating SDEs (other than YUIMA).
Dear Murat Koptur
Kindly, check the following link where you can see the list of softwares that can run stochastic differential equations and how many times they were cited in the literature. This can help you to give you an insight of the popularity of a particular software/package.
https://www.swmath.org/?term=stochastic%20differential%20equations
R-programming language is a very powerful software that can perform this assignment
Here you can find a Python sofware package that implements strong numerical methods of orders 0.5 (Euler), 1.0 (Milstein), 1.5, 2.0, 2.5, 3.0 for Ito SDEs with non-commutative noise:
https://diffjournal.spbu.ru/EN/numbers/2021.1/article.1.5.html
Here you can find all about strong approximation of iterated Ito and Stratonovich stochastic integral (in application to numerical integration of Ito SDEs and semilinear SPDEs):
https://arxiv.org/abs/2003.14184
Hope this is helpful!
Here you can find a Python sofware package that implements strong numerical methods of orders 0.5 (Euler), 1.0 (Milstein), 1.5, 2.0, 2.5, 3.0 for Ito SDEs with non-commutative noise:
https://diffjournal.spbu.ru/EN/numbers/2021.1/article.1.5.html
Here you can find all about strong approximation of iterated Ito and Stratonovich stochastic integral (in application to numerical integration of Ito SDEs and semilinear SPDEs):
https://arxiv.org/abs/2003.14184
Hope this is helpful!
Julia differential equation solvers have high order and adaptive methods (https://diffeq.sciml.ai/stable/tutorials/sde_example/). But more importantly, these implementations are compatible with automatic differentiation, making it easy to do things like gradient descent for doing parameter estimation and model calibration. Tutorials of this can be found in the Julia SciML libraries, such as https://sensitivity.sciml.ai/dev/sde_fitting/optimization_sde/. The other advantage of course is performance, where the Julia performance over Python and MATLAB solvers is a few orders of magnitude (https://benchmarks.sciml.ai/html/MultiLanguage/wrapper_packages.html)
Few years ago I had to solve SDE, DDE and SDDE. I have benchmarked software languages such as Scilab, Matlab, R, Python, Maxima and Julia. Eventually, I preferred Julia for several reasons.
One main reason is the user community which is incredibly active and helpful.
The syntax of those languages is quite similar (basically the difference from Turkish to Azeribarjiani). In one day you can move from R to Julia.
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