Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 866 products
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QDD50 - 07/15/2009
Bertacchi, D.; Zucca, F.
Approximating Critical Parameters of Branching Random Walks | Abstract | | Given a branching random walk on a graph, we consider two kinds of truncations:
either by inhibiting the reproduction outside a subset of vertices or by allowing at most m particles per vertex. We investigate the convergence of weak and strong critical parameters of these truncated branching random walks to the analogous parameters of the original branching random walk. As a corollary, we apply our results to the study of the strong critical parameter of a branching random walk restricted to the cluster of a Bernoulli bond percolation. |
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QDD45 - 07/10/2009
Pagani, C.D. ; Pierotti, D.
Variational methods for nonlinear Steklov eigenvalue problems with an indefinite weight function | Abstract | | We consider the problem of finding a harmonic function $u$ in a bounded domain $ om subset R^n$, $n ge 2$, satisfying a nonlinear boundary condition of the form $ partial_{ nu}u(x)= lambda mu(x)h(u(x))$, $x in partial om$ where $ mu$ changes sign and $h$ is an increasing function with superlinear, subcritical growth at infinity. We study the solvability of the problem depending on the parameter $ lambda$ by using min-max methods.
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QDD44 - 04/24/2009
Maluta, E.; Papini, P.L.
Estimates for Kottman s separation constant in reflexive Banach spaces | Abstract | | In reflexive Banach spaces which possess some degree of uniform convexity,
we obtain estimates for Kottman s separation constant in terms of the
corresponding modulus. |
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QDD43 - 04/17/2009
Berchio, E. ; Gazzola, F. ; Pierotti, D.
Gelfand type elliptic problems under Steklov boundary conditions | Abstract | | For a Gelfand type semilinear elliptic equation we extend some known results for the Dirichlet
problem to the Steklov problem.
This extension requires some new tools, such as non-optimal Hardy inequalities, and discovers some new phenomena, in particular a di fferent behavior of the branch of solutions and three kinds of blow-up for large solutions in critical growth equations. We also show that small values of the boundary parameter play against strong growth of the nonlinear source. |
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QDD42 - 04/06/2009
Ballestra, L.V.; Sgarra, C.
The Evaluation of American Options in a Stochastic Volatility Model with Jumps: a Finite Element Approach | Abstract | | In the present paper we consider the problem of pricing American options in the framework of a well-known stochastic volatility model with jumps, the Bates model. According to this model the asset price is assumed to follow a jump-diffusion equation in which the jump term consists of a Lévy process of compound Poisson type, while the volatility is modeled as a CIR-type process correlated with the asset price. In this model the American option valuation is reduced to a final-free-boundary-value partial integro-differential problem. Using a Richardson extrapolation technique this problem is reduced to a partial integro-differential problems with fixed boundary. Then the transformed problem is solved using an ad-hoc finite element method which efficiently combines an operator splitting technique with a non-uniform mesh of right-angled triangles. Numerical experiments are presented showing that the option pricing algorithm developed in this paper is very accurate and fast. |
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QDD41 - 01/22/2009
Giardina, F.; Guglielmi, A.; Quintana, F. A.; Ruggeri, F.
Bayesian first order autoregressive latent variable models for multiple binary sequences | Abstract | | Longitudinal clinical trials often collect long sequences of binary data monitoring a disease process over time. Our application is a
medical study conducted by VACURG to assess the effectiveness of a chemioterapic treatment (thiotepa) in preventing recurrence on subjects
affected by bladder cancer. We propose a generalized linear model with latent autoregressive structure for longitudinal binary data following a Bayesian approach. We describe a suitable posterior simulation scheme and discuss inference and sensitivity issues for the bladder
cancer data. |
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QDD40 - 11/06/2008
Boccellari, T.; Tomarelli, F.
About well-posedness of optimal segmentation for Blake & Zisserman functional | Abstract | | We focus well-posedness in the minimization of a second order free discontinuity problem. Various examples of multiplicity for minimizers are shown. |
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QDD39 - 10/27/2008
Bassetti, F. ; Ladelli, L. ; Matthes, D.
Central limit theorem for a class of one-dimensional kinetic equations | Abstract | | We introduce a class of Boltzmann equations on the real line, which constitute extensions of the classical Kac caricature. The collisional gain operators are defined by smoothing transformations with quite general properties. By establishing a connection to the central limit problem, we are able to prove long-time convergence of the equation s solutions towards a limit distribution. If the initial condition for the Boltzmann equation belongs to the domain of normal attraction of a certain stable law nu_alpha, then the limit is a scale mixture of nu_alpha. Under some additional assumptions, explicit exponential rates for the convergence to equilibrium in Wasserstein metrics are calculated, and strong convergence of the probability densities is shown.
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