Scientific Reports
The preprint collection of the Department of Mathematics.
Full-text generally not available for preprints prior to may 2006.
Found 868 products
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QDD48 - 07/15/2009
Bertacchi, D. ; Zucca, F.
Critical behaviors and critical values of branching random walks on multigraphs | Abstract | | We consider weak and strong survival for branching random walks on multigraphs with
bounded degree. We prove that, at the strong critical value, the process dies out locally almost surely. We relate the weak critical value to a geometrical parameter of the multigraph. For
a large class of multigraphs (which enlarges the class of quasi-transitive or regular graphs) we
prove that, at the weak critical value, the process dies out globally almost surely. Moreover for the same class we prove that the existence of a pure weak phase is equivalent to nonamenability.
The results are extended to branching random walks on weighted graphs. |
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QDD49 - 07/15/2009
Bertacchi, D. ; Zucca, F.
Characterization of critical values of branching random walks on weighted graphs through infinite-type branching processes | Abstract | | We study the branching random walk on weighted graphs; site-breeding and edge-breeding branching random walks on graphs are seen as particular cases. Two kinds of survival can be identi¯ed: a weak survival (with positive probability there is at least one particle alive somewhere at any time) and a strong survival (with positive probability the colony survives by returning in¯nitely often to a ¯xed site). The behavior of the process depends on the value of a certain parameter which controls the birth rates; the threshold between survival and (almost sure)
extinction is called critical value. We describe the strong critical value in terms of a geometrical parameter of the graph. We characterize the weak critical value and relate it to another geometrical parameter. We prove that, at the strong critical value, the process dies out locally almost surely; while, at the weak critical value, global survival and global extinction are both possible. |
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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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