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Eigenvalue, Majorization, Matrix absolute value, Matrix inequality, Matrix norm, Normal matrix, Positive semidefinite matrix, Singular value, Spread, Wielandt inequality.. AMS
n ≥ 2, and obtain an inequality satisfied by the real and imaginary part of every eigenvalue of A (Section 3).In turn, this inequality gives rise to a region in the complex plane
Walsh’s theory of martingale measures in order to deal with stochastic partial differential equations that are second order in time, such as the wave equation and the beam equation,
We will see in Section 4.1 that, assuming the Lifshitz tail effect in [ 12 ] , our result indeed derives the correct upper bound of the quenched asymptotics for the Brownian
The proof of Theorem 3 is based on Burkholder’s technique, which reduces the problem of proving a martingale inequality to finding a certain spe- cial function.. The description of
Continuous Ocone martingales as weak limits of rescaled martingales. Some invariance properties of the laws of
So, using the martingale property of M we see that N is a local martingale. The equivalence between i) and ii) in the above proposition corresponds to a well known
We present a tail inequality for suprema of empirical processes generated by vari- ables with finite ψ α norms and apply it to some geometrically ergodic Markov chains to derive
