Precise Asymptotics of Small Eigenvalues of Reversible Diffusions in the Metastable Regime

Metastability in Reversible Diffusion Processes Ii. Precise Asymptotics for Small Eigenvalues

Marginal density expansions for diffusions and stochastic volatility, part II: Applications

In [17] we discussed density expansions for multidimensional diffusions ( X, . . . , X ) , at fixed time T and projected to their first l coordinates, in the small noise regime. Global conditions were found which replace the well-known ”not-in-cutlocus” condition known from heat-kernel asymptotics. In the present paper we discuss financial applications; these include tail and implied volatility...

2 01 5 Varadhan ’ s formula , conditioned diffusions , and local volatilities

Motivated by marginals-mimicking results for Itô processes [15, 21] via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely L(Zt|Yt = y) if X· = (Y·, Z·). To do so, we revisit Varadhan-type estimates in a small-noise regime, studying the d...

Localization of Eigenvalues in Small Specified Regions of Complex Plane by State Feedback Matrix

This paper is concerned with the problem of designing discrete-time control systems with closed-loop eigenvalues in a prescribed region of stability. First, we obtain a state feedback matrix which assigns all the eigenvalues to zero, and then by elementary similarity operations we find a state feedback which assigns the eigenvalues inside a circle with center   and radius. This new algorithm ca...

Spectral asymptotics of the Dirichlet Laplacian in a conical layer

The spectrum of the Dirichlet Laplacian on conical layers is analysed through two aspects: the infiniteness of the discrete eigenvalues and their expansions in the small aperture limit. On the one hand, we prove that, for any aperture, the eigenvalues accumulate below the threshold of the essential spectrum: For a small distance from the essential spectrum, the number of eigenvalues farther fro...