We establish integral tests and laws of the iterated logarithm at 0 and at +∞, for the upper envelope of positive self-similar Markov processes. Our arguments are based on the Lamperti representation, time reversal arguments and on the study of the upper envelope of their future infimum due to Pardo [19]. These results extend integral test and laws of the iterated logarithm for Bessel processes...

assessment of compensation for the reduction in the value of the currency in case of the financial dowry is the issues that were not previously. the creation of credit money and their value redution caused that compensation for the value of money be considered as a means to preserve the value of money in financial liabilities arise such as dowry. in this regard, there was an waver to article 10...

In this paper, a new actuator fault tolerant control strategy is proposed for nonlinear Takagi-Sugeno systems. The proposed control law uses the estimated fault and the error between the faulty system state and a reference system state. A proportional integral observer with unknown inputs is conceived in order to estimate simultaneously states and actuator faults. The problem of design of obser...

In this contribution, we report the generation of 17-μJ mid-infrared (MIR) pulses with duration of 70 fs and bandwidth of 550 nm centered at 3.75 μm at 1-kHz repetition rate, by a two-stage femtosecond optical parametric amplifier utilizing 4H-silicon carbide crystal as the nonlinear medium. The crystal is selected as it processes orders of magnitude higher damage threshold than traditional MIR...

Abstract We prove a moment identity on the Wiener space that extends the Skorohod isometry to arbitrary powers of the Skorohod integral on the Wiener space. As simple consequences of this identity we obtain sufficient conditions for the Gaussianity of the law of the Skorohod integral and a recurrence relation for the moments of second order Wiener integrals. We also recover and extend the suffi...

It is well-known from linear systems theory that an integral control law is needed for asymptotic set-point regulation under parameter perturbations. This paper presents a similar result for a class of nonlinear systems in the presence of an unknown equilibrium due to uncertain nonlinearities and dynamic uncertainties. Both partial-state and output feedback cases are considered. A procedure for...

We establish integral tests and laws of the iterated logarithm for the lower envelope of positive self-similar Markov processes at 0 and +∞. Our proofs are based on the Lamperti representation and time reversal arguments. These results extend laws of the iterated logarithm for Bessel processes due to Dvoretsky and Erdös [11], Motoo [17] and Rivero [18]. time reversal, integral test, law of the ...