A sharp c\`adl\`ag property for jump diffusions and dynamic programming principle

Given a standard Brownian motion $W$ and a stationary Poisson point process $p$ with characteristic measure $\nu(dz)$, both with values in ${\mathbb R}^d$, we consider the following SDE of It\^o's type \begin{align*} &dX_{t}=b\left(r, X_{r}\right) dr + \alpha\left(r, X_{r} \right) dW_r+ \int_{ |z| \le 1}g\left(X_{r-},r,z\right)\tilde{N}_p\left(dr,dz\right) + \int_{ |z| >1 } f\left(X_{r-},r,z\right){N}_p\left(dr,dz\right), \end{align*} where $X_s=x\in\mathbb{R}^d,\,0\le s \le t \le T.$ Here $N_p$ [resp., $\tilde{N}_p$] is the Poisson [resp., compensated Poisson] random measure associated with $p$. We require the coefficients $b$, $\alpha$, and $g$ to satisfy Lipschitz--type conditions in the $x-$variable, ensuring the existence of a pathwise unique strong solution $X = (X^{s,x}_t)_{t\ge s}$. We prove, in particular, that there exists a sharp version of $X$, i.e., there exists an almost sure event $\Omega'$ such that, for every $\omega \in \Omega'$, the map $(s,x,t)\mapsto X^{s,x}_t(\omega)$ is c\`adl\`ag in $s$ (for $t$ and $x$ fixed), c\`adl\`ag in $t$ (for $s$ and $x$ fixed) and continuous in $x$ (for $s$ and $t$ fixed). In the case of SDEs with only small jumps, i.e., with $f\equiv0$, this result solves an open problem which also appears in Kunita's book on stochastic flows. In our proof, we deal with non-separable spaces of c\`adl\`ag functions involving supremum norms and, when $f\equiv 0$, we employ an extension of the c\`adl\`ag criterion by Bezandry and Fernique, which is proved in the appendix. We then extend our approach to encompass controlled SDEs having also a large-jumps component. Using our sharp stochastic flow we obtain a new dynamic programming principle, whose proof is of independent interest

On the Kolmogorov equation associated with Volterra equations and Fractional Brownian Motion

We consider a Volterra convolution equation in $\mathbb{R}^d$ perturbed with an additive fractional Brownian motion of Riemann-Liouville type with Hurst parameter $H\in (0,1)$. We show that its solution solves a stochastic partial differential equation (SPDE) in the Hilbert space of square-integrable functions. Such an equation motivates our study of an unconventional class of SPDEs requiring an original extension of the drift operator and its Fr\'echet differentials. We prove that these SPDEs generate a Markov stochastic flow which is twice Fr\'echet differentiable with respect to the initial data. This stochastic flow is then employed to solve, in the classical sense of infinite dimensional calculus, the path-dependent Kolmogorov equation corresponding to the SPDEs. In particular, we associate a time-dependent infinitesimal generator with the fractional Brownian motion. In the final section, we show some obstructions in the analysis of the mild formulation of the Kolmogorov equation for SPDEs driven by the same infinite dimensional noise. This problem, which is relevant to the theory of regularization-by-noise, remains open for future research

Un pericoloso terrorista

[Abstract non disponibile

Le nuove frontiere dell’interesse pubblico nella dinamica del diritto penale.

Il testo riporta l’intervento dell’autore al Convegno «L’innovazione istituzionale: grandi disegni o vere riforme?», svolto a Matera il 12 aprile 2002. Trattando le qualifiche soggettive degli agenti pubblici, vengono suggeriti nuovi percorsi interpretativi dello statuto penale della pubblica amministrazione. In particolare, l’analisi si sofferma su temi quali l’autonomia del diritto penale rispetto alle disposizioni di diritto amministrativo; il «quando» e il «come» intervenire con lo strumento della pena per la tutela degli interessi legati all’amministrazione pubblica in un’ottica costituzionalmente orientata

Massimo Pavarini e le città sicure. Patricia Victoria Perello’ intervista Massimo Pavarini. Universitad Nacional de Mar del Plata, Giugno 2013

[Massimo Pavarini and the Urban Security] Urban security, perception of security, Government of public spaces, urban development, lived and consumed city, new citizenship, conflict dislocation, inclusion and exclusion policy, stereotypes, to be in politics: a criminologist life and his social commitment in one of the last interviews of Massimo Pavarini.

La geografia dei diritti

Sommario: 1. Identità europea. – 2. Dimensione nazionale. – 3. Dimensione europea. – 4. Dimensione globale. – 5. Senza memoria. – 6. Senza diritti. – 7. Senza Europa

Multi-view coding of local features in visual sensor networks

Local visual features extracted from multiple camera views are employed nowadays in several application scenarios, such as object recognition, disparity matching, image stitching and many others. In several cases, local features need to be transmitted or stored on resource-limited devices, thus calling for efficient coding techniques. While recent works have addressed the problem of efficiently compressing local features extracted from still images or video sequences, in this paper we propose and evaluate an architecture for coding features extracted from multiple, overlapping views. The proposed Multi-View Feature Coding architecture can be applied to either real-valued or binary features, and allows to obtain bitrate reductions in the order of 10-20% with respect to simulcast coding

Comparison of the effects of hyaluronidase and hyaluronic acid on probiotics growth

Hyaluronic acid has several clinical applications. Recent evidences suggested antimicrobial properties against several pathogens. The aim of the present survey was to evaluate the effect of hyaluronic acid, alone or in combination with hyaluronidase, on protechnological or probiotic strains