On moduli of smoothness of fractional order

In this paper we consider the properties of moduli of smoothness of fractional order. The main result of the paper describes the equivalence of the modulus of smoothness and a function from some class.

On the boundedness on inhomogeneous Lipschitz spaces of fractional integrals, singular integrals and hypersingular integrals associated to non-doubling measures on metric spaces

In this paper we prove T1 type necessary and sufficient conditions for the boundedness on inhomogeneous Lipschitz spaces of fractional integrals and singular integrals defined on a measure metric space whose measure satisfies a n-dimensional growth. We also show that hypersingular integrals are bounded on these spaces.

HSU-Robbins and Spitzer's theorems for the variations of fractional Brownian motion

Using recent results on the behavior of multiple Wiener-Itô integrals based on Stein's method, we prove Hsu-Robbins and Spitzer's theorems for sequences of correlated random variables related to the increments of the fractional Brownian motion.

Sharp weighted bounds for fractional integral operators

The relationship between the operator norms of fractional integral operators acting on weighted Lebesgue spaces and the constant of the weights is investigated. Sharp bounds are obtained for both the fractional integral operators and the associated fractional maximal functions. As an application improved Sobolev inequalities are obtained. Some of the techniques used include a sharp off-diagonal version of the extrapolation theorem of Rubio de Francia and characterizations of two-weight norm inequalities.

Hours worked - Productivity puzzle: identification in fractional integration settings

A recent finding of the structural VAR literature is that the response of hours worked to a technology shock depends on the assumption on the order of integration of the hours. In this work we relax this assumption, allowing for fractional integration and long memory in the process for hours and productivity. We find that the sign and magnitude of the estimated impulse responses of hours to a positive technology shock depend crucially on the assumptions applied to identify them. Responses estimated with short-run identification are positive and statistically significant in all datasets analyzed. Long-run identification results in negative often not statistically significant responses. We check validity of these assumptions with the Sims (1989) procedure, concluding that both types of assumptions are appropriate to recover the impulse responses of hours in a fractionally integrated VAR. However, the application of longrun identification results in a substantial increase of the sampling uncertainty. JEL Classification numbers: C22, E32. Keywords: technology shock, fractional integration, hours worked, structural VAR, identification

Is the observed persistence spurious? A test for fractional integration versus short memory and structural breaks

Although it is commonly accepted that most macroeconomic variables are nonstationary, it is often difficult to identify the source of the non-stationarity. In particular, it is well-known that integrated and short memory models containing trending components that may display sudden changes in their parameters share some statistical properties that make their identification a hard task. The goal of this paper is to extend the classical testing framework for I(1) versus I(0)+ breaks by considering a a more general class of models under the null hypothesis: non-stationary fractionally integrated (FI) processes. A similar identification problem holds in this broader setting which is shown to be a relevant issue from both a statistical and an economic perspective. The proposed test is developed in the time domain and is very simple to compute. The asymptotic properties of the new technique are derived and it is shown by simulation that it is very well-behaved in finite samples. To illustrate the usefulness of the proposed technique, an application using inflation data is also provided.

Differential equations driven by fractional Brownian motion

A global existence and uniqueness result of the solution for multidimensional, time dependent, stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H> is proved. It is shown, also, that the solution has finite moments. The result is based on a deterministic existence and uniqueness theorem whose proof uses a contraction principle and a priori estimates.

Nitric oxide synthase (NOS) inhibition for one week improves renal sodium and water excretion in cirrhotic rats with ascites

Normalization of the increased vascular nitric oxide (NO) generation with low doses of NG-nitro-L-arginine methyl ester (L-NAME) corrects the hemodynamic abnormalities of cirrhotic rats with ascites. We have undertaken this study to investigate the effect of the normalization of vascular NO production, as estimated by aortic cyclic guanosine monophosphate (cGMP) concentration and endothelial nitric oxide synthase (eNOS) protein expression in the aorta and mesenteric artery, on sodium and water excretion. Rats with carbon tetrachloride-induced cirrhosis and ascites were investigated using balance studies. The cirrhotic rats were separated into two groups, one receiving 0.5 mg/kg per day of L-NAME (CIR-NAME) during 7 d, whereas the other group (CIR) was administrated the same volume of vehicle. Two other groups of rats were used as controls, one group treated with L-NAME and another group receiving the same volume of vehicle. Sodium and water excretion was measured on days 0 and 7. On day 8, blood samples were collected for electrolyte and hormone measurements, and aorta and mesenteric arteries were harvested for cGMP determination and nitric oxide synthase (NOS) immunoblotting. Aortic cGMP and eNOS protein expression in the aorta and mesenteric artery were increased in CIR as compared with CIR-NAME. Both cirrhotic groups had a similar decrease in sodium excretion on day 0 (0.7 versus 0.6 mmol per day, NS) and a positive sodium balance (+0.9 versus +1.2 mmol per day, NS). On day 7, CIR-NAME rats had an increase in sodium excretion as compared with the CIR rats (sodium excretion: 2.4 versus 0.7 mmol per day, P < 0.001) and a negative sodium balance (-0.5 versus +0.8 mmol per day, P < 0.001). The excretion of a water load was also increased after L-NAME administration (from 28+/-5% to 65+/-7, P < 0.05). Plasma renin activity, aldosterone and arginine vasopressin were also significantly decreased in the CIR-NAME, as compared with the CIR rats. The results thus indicate that normalization of aortic cGMP and eNOS protein expression in vascular tissue is associated with increased sodium and water excretion in cirrhotic rats with ascites.

Power variation of some integral fractional processes

We consider the asymptotic behaviour of the realized power variation of processes of the form ¿t0usdBHs, where BH is a fractional Brownian motion with Hurst parameter H E(0,1), and u is a process with finite q-variation, q<1/(1¿H). We establish the stable convergence of the corresponding fluctuations. These results provide new statistical tools to study and detect the long-memory effect and the Hurst parameter.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.

Stochastic delay differential equations driven by fractional Brownian motion with Hurst parameter H 1/2

We consider the Cauchy problem for a stochastic delay differential equation driven by a fractional Brownian motion with Hurst parameter H>¿. We prove an existence and uniqueness result for this problem, when the coefficients are sufficiently regular. Furthermore, if the diffusion coefficient is bounded away from zero and the coefficients are smooth functions with bounded derivatives of all orders, we prove that the law of the solution admits a smooth density with respect to Lebesgue measure on R.

Altered nitrogen balance and decreased urea excretion in male rats fed cafeteria diet are related to arginine availability

Hyperlipidic diets limit glucose oxidation and favor amino acid preservation, hampering the elimination of excess dietary nitrogen and the catabolic utilization of amino acids.We analyzed whether reduced urea excretion was a consequence of higherNO ; (nitrite,nitrate, and other derivatives) availability caused by increased nitric oxide production in metabolic syndrome. Rats fed a cafeteria diet for 30 days had a higher intake and accumulation of amino acid nitrogen and lower urea excretion.There were no differences in plasma nitrate or nitrite. NO and creatinine excretion accounted for only a small part of total nitrogen excretion. Rats fed a cafeteria diet had higher plasma levels of glutamine, serine, threonine, glycine, and ornithinewhen comparedwith controls,whereas arginine was lower. Liver carbamoyl-phosphate synthetase I activity was higher in cafeteria diet-fed rats, but arginase I was lower. The high carbamoyl-phosphate synthetase activity and ornithine levels suggest activation of the urea cycle in cafeteria diet-fed rats, but low arginine levels point to a block in the urea cycle between ornithine and arginine, thereby preventing the elimination of excess nitrogen as urea. The ultimate consequence of this paradoxical block in the urea cycle seems to be the limitation of arginine production and/or availability.

Abnormalities of sodium excretion and other disorders of renal function in fulminant hepatic failure

Renal function was evaluated in 40 patients with fulminant hepatic failure, They were divided into two groups on the basis of glomerular filtration rates greater than 40 ml/min or less than 25 ml/min. A number of patients in group 1 had markedly abnormal renal retention of sodium together with a reduced free water clearance and low potassium excretion which could be explained by increased proximal tubular reabsorption of sodium. The patients in group 2 had evidence that renal tubular integrity was maintained when the glomerular filtration rate was greater than or equal ml/min (functional renal failure), but evidence of tubular damage was present when this was less than 3 ml/min (acute tubular necrosis).

The effects of milk as a food matrix for polyphenols on the excretion profile of cocoa (-)-Epicatechin metabolites in healthy humans subjects

The effect of different food matrices on the metabolism and excretion of polyphenols is uncertain. The objective of the study was to evaluate the possible effect of milk on the excretion of (2)-epicatechin metabolites from cocoa powder after its ingestion with and without milk. Twenty-one volunteers received the following three test meals each in a randomised cross-over design with a 1-week interval between meals: (1) 250 ml whole milk as a control; (2) 40 g cocoa powder dissolved in 250 ml whole milk (CC-M); (3) 40 g cocoa powder dissolved in 250 ml water (CC-W). Urine was collected before consumption and during the 0-6, 6-12 and 12-24 h periods after consumption. (2)-Epicatechin metabolite excretion was measured using liquid chromatography-MS. One (2)-epicatechin glucuronide and three (2)-epicatechin sulfates were detected in urine excreted after the intake of the two cocoa beverages (CC-M and CC-W). The results show that milk does not significantly affect the total amount of metabolites excreted in urine. However, differences in metabolite excretion profiles were observed; there were changes in the glucuronide and sulfate excretion rates, and the sulfation position between the period of excretion and the matrix. The matrix in which polyphenols are consumed can affect their metabolism and excretion, and this may affect their biological activity. Thus, more studies are needed to evaluate the effect of these different metabolite profiles on the body.