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Small-time behaviour of Lévy processes
Get PDFIn this paper a necessary and sufficient condition is established for the probability that a Lévy process is positive at time t to tend to 1 as t tends to 0. This condition is expressed in terms of the characteristics of the process, and is also shown to be equivalent to two probabilistic statements about the behaviour of the process for small time t
On the problem of stochastic integral representations of functionals of the Browian motion II
Get PDFFor functionals of the Brownian motion~, we propose a method for finding stochastic integral representations based on the It\^o formula for the stochastic integral associated with~. As an illustration of the method, we consider functionals of the ``maximal" type: , , , and , where , with , , and , , and are {\em non}-Markov times: ~is the time of the last zero of Brownian motion on and ~is a time when the Brownian motion achieves its maximal value on
Rank analysis of the anisotropic inverse conductivity problem
Get PDFAnisotropic conductivity arises in bio-medical EIT, for example in muscle tissue, however the anisotropic inverse conductivity problem can be solved uniquely only up to a diffeomorphism which fixes all points on the boundary. Although a scalar conductivity can be reconstructed from current and voltage measurements, extra information must be provided to uniquely recover the full symmetric tensor field in the anisotropic case. Rank analysis of the sensitivity matrix reveals that fixing the mesh a-priori selects one of the infinity of possible diffeomorphisms, but may lead to a wrong solution. Hence one should not attempt solving the problem for a fixed mesh, and we suggest a procedure to resolve the ambiguity by imposing some constraints which restore uniqueness of the solution
On Some Concepts of Residuals
No full textWe introduce confidence residuals and standardised confidence residuals. These residuals may be especially useful for asymmetric and multimodal distributions
A Jacobi-Davidson type projection method for nonlinear eigenvalue problems
Get PDFThis paper discusses a projection method for nonlinear eigenvalue problems. The subspace of approximants is constructed by a Jacobi–Davidson-type approach, and the arising eigenproblems of small dimension are solved by safeguarded iteration. The method is applied to a rational eigenvalue problem governing the vibrations of tube bundle immersed in an inviscid compressible fluid
Geometric methods for anisotopic inverse boundary value problems.
Get PDFElectromagnetic fields have a natural representation as differential forms. Typically the measurement of a field involves an integral over a submanifold of the domain.
Differential forms arise as the natural objects to integrate over submanifolds of each dimension. We will see that the (possibly anisotropic) material response to a field can be naturally associated with a Hodge star operator. This geometric point of view is now well established in computational electromagnetism,
particularly by Kotiuga, and by Bossavit and and others. The essential point is that Maxwell’s equations can be formulated in a context independent of the ambient Euclidean metric. This approach has theoretical
elegance and leads to simplicity of computation.
In this paper we will review the geometric formulation of the (scalar) anisotropic inverse conductivity problem, amplifying some of the geometric points made in Uhlmann’s
paper in this volume. We will go on to consider generalizations of this anisotropic inverse boundary value problem to systems of Partial Differential Equation, including the result of Joshi and the author on the inverse boundary value problem for harmonic k-forms
A generic identification theorem for groups of finite Morley rank
No full textThe paper contains a final identification theorem for the ‘generic’ -groups of finite Morley rank
Modular Lie representations of groups of prime order
No full textLet K be a field of prime characteristic p and let G be a group of order p. For any finite-dimensional KG-module V and any positive integer n let L n (V) denote the nth homogeneous component of the free Lie K-algebra generated by (a basis of) V. Then L n (V) can be considered as a KG-module, called the nth Lie power of V. The main result of the paper is a formula which describes the module structure of L n (V) up to isomorphism
Irregular isomonodromic for Garnier systems and Okamoto's canonical transformations
No full textThe paper describes the Garnier systems as isomonodromic deformation equations of a linear system with a simple pole at 0 and a Poincaré rank 1 singularity at infinity. The extension of Okamoto's birational canonical transformations to the Garnier systems in more than one variable and to the Schlesinger systems is discussed