Exponential integrability of stochastic convolutions

Sucient conditions are found for stochastic convolution integrals driven by a Wiener process in a Hilbert space to belong to the Orlicz space expL2; standard exponential tail estimates follow from these results. Proofs are based on the extrapolation theory and are rather simple.</p

Da Prato-Zabczyk's maximal inequality revisited. I.

summary:Existence, uniqueness and regularity of mild solutions to semilinear nonautonomous stochastic parabolic equations with locally lipschitzian nonlinear terms is investigated. The adopted approach is based on the factorization method due to Da Prato, Kwapień and Zabczyk

Credit growth and financial stability in the Czech Republic

The Czech Republic had experienced a credit boom similar to those in other converging economies in the pre-crisis years. Nevertheless, the consequences of this credit boom were limited as was the impact of the global crisis on domestic financial institutions. This paper describes the developments in the Czech banking sector and explains how the tough macroeconomic environment in the Czech Republic acted as a strong tool of macroprudential policy. It concludes that although it is difficult to tame credit booms in small converging economies, a concerted set of microprudential and macroprudential measures, including monetary and fiscal ones, may ensure some success.Banks&Banking Reform,Debt Markets,Currencies and Exchange Rates,Access to Finance,Emerging Markets

A note on maximal inequality for stochastic convolutions

summary:Using unitary dilations we give a very simple proof of the maximal inequality for a stochastic convolution $$\int ^t_0 S(t-s)\psi (s)\mathrm{d}W(s)$$ driven by a Wiener process $W$ in a Hilbert space in the case when the semigroup $S(t)$ is of contraction type

Excepcionalidad y cainismo:Los nudos de la memoria en España

summary:We revisit the proof of existence of weak solutions of stochastic differential equations with continuous coeficients. In standard proofs, the coefficients are approximated by more regular ones and it is necessary to prove that: i) the laws of solutions of approximating equations form a tight set of measures on the paths space, ii) its cluster points are laws of solutions of the limit equation. We aim at showing that both steps may be done in a particularly simple and elementary manner

Seasonality of human sleep: Polysomnographic data of a neuropsychiatric sleep clinic

While short-term effects of artificial light on human sleep are increasingly being studied, reports on long-term effects induced by season are scarce. Assessments of subjective sleep length over the year suggest a substantially longer sleep period during winter. Our retrospective study aimed to investigate seasonal variation in objective sleep measures in a cohort of patients living in an urban environment. In 2019, three-night polysomnography was performed on 292 patients with neuropsychiatric sleep disturbances. Measures of the diagnostic second nights were averaged per month and analyzed over the year. Patients were advised to sleep "as usual" including timing, except alarm clocks were not allowed. Exclusion criteria: administration of psychotropic agents known to influence sleep (N = 96), REM-sleep latency > 120 min (N = 5), technical failure (N = 3). Included were 188 patients: [46.6 +/- 15.9 years (mean +/- SD); range 17-81 years; 52% female]; most common sleep-related diagnoses: insomnia (N = 108), depression (N = 59) and sleep-related breathing disorders (N = 52). Analyses showed: 1. total sleep time (TST) longer during winter than summer (up to 60 min; not significant); 2. REM-sleep latency shorter during autumn than spring (about 25 min, p = 0.010); 3. REM-sleep longer during winter than spring (about 30 min, p = 0.009, 5% of TST, p = 0.011); 4. slow-wave-sleep stable winter to summer (about 60-70 min) with 30-50 min shorter during autumn (only significant as % of TST, 10% decrease, p = 0.017). Data suggest seasonal variation in sleep architecture even when living in an urban environment in patients with disturbed sleep. If replicated in a healthy population, this would provide first evidence for a need to adjust sleep habits to season

Vitality and germination of lemon balm (<i>Melissa officinalis</i> L.) seeds

In 2012-2014, the germination ability of lemon balm seeds were tested. The investigated seeds were obtained from the lemon balm breeding project conducted at the Institute of natural Fibres & Medicinal Plants of Poznań, Poland. The germination rate was done by using ISTA seed germination rules and the high fluctuation of germination rate was observed. Low rate of germination usually disqualificates the seed material. Thus, the anatomy of the investigated lemon balm seeds was analyzed by scanning electron microscopy (SEM) and tetrazolium test was done. SEM analysis showed accurate morphological structure of all seed parts. The embryos, endosperm and testa were well and correctly developed. Seed coat was typical for all species of Lamiaceae. Abnormal seed part were not found. Tetrazolium test revealed the high rate of vitality of the investigated strain seeds. Thus, other useful tests should be recommended before seed disqualification will be done in case of low germination rate

Maximal LpL^p-regularity for stochastic evolution equations

We prove maximal $L^p$-regularity for the stochastic evolution equation \{{aligned} dU(t) + A U(t)\, dt& = F(t,U(t))\,dt + B(t,U(t))\,dW_H(t), \qquad t\in [0,T], U(0) & = u_0, {aligned}. under the assumption that $A$ is a sectorial operator with a bounded $H^\infty$-calculus of angle less than $\frac12\pi$ on a space $L^q(\mathcal{O},\mu)$. The driving process $W_H$ is a cylindrical Brownian motion in an abstract Hilbert space $H$. For $p\in (2,\infty)$ and $q\in [2,\infty)$ and initial conditions $u_0$ in the real interpolation space \XAp we prove existence of unique strong solution with trajectories in L^p(0,T;\Dom(A))\cap C([0,T];\XAp), provided the non-linearities F:[0,T]\times \Dom(A)\to L^q(\mathcal{O},\mu) and B:[0,T]\times \Dom(A) \to \g(H,\Dom(A^{\frac12})) are of linear growth and Lipschitz continuous in their second variables with small enough Lipschitz constants. Extensions to the case where $A$ is an adapted operator-valued process are considered as well. Various applications to stochastic partial differential equations are worked out in detail. These include higher-order and time-dependent parabolic equations and the Navier-Stokes equation on a smooth bounded domain \OO\subseteq \R^d with $d\ge 2$. For the latter, the existence of a unique strong local solution with values in (H^{1,q}(\OO))^d is shown.Comment: Accepted for publication in SIAM Journal on Mathematical Analysi