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It is known that for a totally positive (TP) matrix, the eigenvalues are positive and distinct and the eigenvector associated with the smallest eigenvalue is totally nonzero and has
Therefore, using the criterion in Proposition 2.1, we induce the following necessary and sufficient conditions.... In this section we will first obtain a result on the CS property
He studies martingales that take self-adjoint matrix values, and he shows that the maximum eigenvalue of the martingale satisfies a tail bound similar to Freedman’s inequality..
As an application of Proposition 2.1, in Corollary 2.1 we also obtain two results on the total occupation time and the almost sure local extinction of the empirical measure process
Now return to the probability in the integrand in the last line in (11) and recall the well-known property of Brownian bridges that conditioning a Brownian motion on its arrival at
Tevzadze , A Semimartingale Bellman equation and the variance- optimal martingale measure, Georgian Math. Tevzadze , A Semimartingale backward equation related to the p
We prove a comparison theorem and maximum principle for a local solution of quasi-linear parabolic stochastic PDEs, similar to the well known results in the deterministic case..
Except for the Toeplitz and Hankel matrices, the common patterned matrices for which the limiting spectral distribution (LSD) are known to exist share a common property–the number
