SOLUTION Multivariate SDE with repeated Eigenvalues

[andreuan]

I am looking forward the solution of multivariate Ornstein–Uhlenbeck differential stochastic equation with repeated eigenvalues.

In particular with
dy=A(y-c)dt +DdW

y is a vector nx1
A is nxn matrix with repeated eigenvalues
c is vector of nx1 of constant
D is a nxm matrix of constant
dW is a mx1 vector independent brownian motion variables

I tried a lot of SDE (stochastic differential equation book) I only find the classic solution of
A with at n different eigenvalues... Some reference please

 

[gtoguy97]

? Unfortunately, there is not much research available on the solution of the multivariate Ornstein–Uhlenbeck differential stochastic equation with repeated eigenvalues. However, you can find some resources that may be helpful in understanding the theory and methods for solving this type of equation. One such resource is a paper by A. Marchesini and P. Protter titled "The Multi-Dimensional Ornstein-Uhlenbeck Process and Its Application to Natural Language Processing" which can be found here: https://link.springer.com/content/pdf/10.1007/s11222-006-9001-9.pdf. Another resource is a book by S.O. Kuznetsov titled "Stochastic Differential Equations with Repeated Eigenvalues and Their Applications" which can be found here: http://www.springer.com/gp/book/9783642093341. Finally, you may also want to check out the following articles: 1. "Stochastic Differential Equation with Repeated Eigenvalues and Their Application to Financial Mathematics" by A.B. Linder and S.O. Kuznetsov (https://link.springer.com/chapter/10.1007/978-3-642-83929-3_7). 2. "Multi-Dimensional Ornstein-Uhlenbeck Processes with Repeated Eigenvalues" by A.V. Skorokhod (http://iopscience.iop.org/article/10.1070/RM2007v062n02ABEH005041/pdf). 3. "Stochastic Differential Equations with Repeated Eigenvalues" by S.P. Novikov (http://www.sciencedirect.com/science/article/pii/S0022247X14002490). Hopefully, these resources will help you find the solution to the multivariate Ornstein–Uhlenbeck differential stochastic equation with repeated eigenvalues.