Lane P. Hughston

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The manifold of pure quantum states can be regarded as a complex projective space endowed with the unitary-invariant Riemannian geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given quantum system can be represented by specific geometrical features that are selected and(More)
A new approach to credit risk modelling is introduced that avoids the use of inaccessible stopping times. Default events are associated directly with the failure of obligors to make contractually agreed payments. Noisy information about impending cash flows is available to market participants. In this framework the market filtration is modelled explicitly,(More)
The phase space of quantum mechanics can be viewed as the complex projective space CP endowed with a Kählerian structure given by the Fubini-Study metric and an associated symplectic form. Therefore, we can interpret the Schrödinger equation as generating a natural Hamiltonian dynamics on CP. Based upon the geometric structure of the quantum phase space we(More)
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the space of all square-integrable functions. More precisely, by consideration of the square-root(More)
An efficient geometric formulation of the problem of parameter estimation is developed, based on Hilbert space geometry. This theory, which allows for a transparent transition between classical and quantum statistical inference, is then applied to the analysis of exponential families of distributions (of relevance to statistical mechanics) and quantum(More)
A new microcanonical equilibrium state is introduced for quantum systems with finite-dimensional state spaces. Equilibrium is characterised by a uniform distribution on a level surface of the expectation value of the Hamiltonian. The distinguishing feature of the proposed equilibrium state is that the corresponding density of states is a continuous function(More)
Dorje C. Brody∗, Lane P. Hughston† and Joanna Syroka∗ ∗Blackett Laboratory, Imperial College, London SW7 2BZ, UK †Department of Mathematics, King’s College London, Strand, London WC2R 2LS, UK (August 13, 2002) The energy-based stochastic extension of the Schrödinger equation is perhaps the simplest mathematically rigourous and physically plausible model for(More)