BV-regularity for the Malliavin Derivative of the Maximum of the Wiener Process

We prove that, on the classical Wiener space, the random variable $\sup_{0\le t \le T} W_t$ admits a measure as second Malliavin derivative, whose total variation measure is finite and singular w.r.t.\ the Wiener measure

Lagrangian flows driven by BVBV fields in Wiener spaces

We establish the renormalization property for essentially bounded solutions of the continuity equation associated to $BV$ fields in Wiener spaces, with values in the associated Cameron-Martin space; thus obtaining, by standard arguments, new uniqueness and stability results for correspondent Lagrangian $L^\infty$-flows. An example related to Neumann elliptic problems is also discussed

Zero noise limits using local times

We consider a well-known family of SDEs with irregular drifts and the correspondent zero noise limits. Using (mollified) local times, we show which trajectories are selected. The approach is completely probabilistic and relies on elementary stochastic calculus only

Inapproximability of Combinatorial Optimization Problems

We survey results on the hardness of approximating combinatorial optimization problems

Some Applications of Coding Theory in Computational Complexity

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs

Well-posedness of Multidimensional Diffusion Processes with Weakly Differentiable Coefficients

We investigate well-posedness for martingale solutions of stochastic differential equations, under low regularity assumptions on their coefficients, widely extending some results first obtained by A. Figalli. Our main results are a very general equivalence between different descriptions for multidimensional diffusion processes, such as Fokker-Planck equations and martingale problems, under minimal regularity and integrability assumptions, and new existence and uniqueness results for diffusions having weakly differentiable coefficients, by means of energy estimates and commutator inequalities. Our approach relies upon techniques recently developed, jointly with L. Ambrosio, to address well-posedness for ordinary differential equations in metric measure spaces: in particular, we employ in a systematic way new representations and inequalities for commutators between smoothing operators and diffusion generators.Comment: Added references to further literature on the subjec

Enforcement of Employment Protection and the hiring behaviour of firms. Evidence from a large Italian region.

This paper investigates the effect of the Employment Protection Legislation (EPL) on the hiring behaviour of the firms when the level of EPL is differentiated by firms size. In this respect, Italy represents an interesting case because workers hired by bigger firms enjoy a stronger protection than workers hired by small firms; the threshold size is fixed by law at 15 employees. A model derives the conditions under which firms decide whether to upsize or not and, in case of upsizing, whether to hire temporary (i.e. workers who are not counted in the threshold, as apprentices in Italy) or permanent workers. The model has been tested using data drawn from the VWH (Veneto Workers History) registered data for firms and workers, from 1982 to 1997, for a large Italian region (i.e. Veneto). Firms close to the threshold are not scared to growth but they are more likely to hire apprentices than permanent workers.Employment Protection, Hiring, Random Effects, Regression Discontinuity Design.

Job Security and New Restrictive Permanent Contracts. Are Spanish Workers More Worried of Losing Their Job?

This paper investigates the impact of the introduction of new restrictive permanent contracts on the perceived job security of the workers in Spain. The perceived job security is strongly influenced by the characteristics of individuals and their distribution within groups. Comparing heterogeneous groups could make the traditional DID estimator biased. To address this issue I combine the propensity score matching DID with a fixed effect estimator. The analysis is conducted using data from the ECHP Survey for Spain from 1995 to 2000. The result is that this reform has a positive impact only for one targeted group, i.e. the young workers and no effect for the others. Several robustness checks are performed.Job security, Firing Costs, Evaluation Policy, Fixed effect estimator.