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41.
Jamil Chaker 《Mathematische Nachrichten》2019,292(11):2316-2337
We consider systems of stochastic differential equations of the form for with continuous, bounded and non‐degenerate coefficients. Here are independent one‐dimensional stable processes with . In this article we research on uniqueness of weak solutions to such systems by studying the corresponding martingale problem. We prove the uniqueness of weak solutions in the case of diagonal coefficient matrices. 相似文献
42.
Shai Shechter 《Journal of Pure and Applied Algebra》2019,223(10):4384-4425
Let be a complete discrete valuation ring with finite residue field of odd characteristic, and let G be a symplectic or special orthogonal group scheme over . For any let denote the ?-th principal congruence subgroup of . An irreducible character of the group is said to be regular if it is trivial on a subgroup for some ?, and if its restriction to consists of characters of minimal -stabilizer dimension. In the present paper we consider the regular characters of such classical groups over , and construct and enumerate all regular characters of , when the characteristic of is greater than two. As a result, we compute the regular part of their representation zeta function. 相似文献
43.
Bilender P. Allahverdiev 《Mathematical Methods in the Applied Sciences》2019,42(1):229-236
In this study, maximal dissipative second‐order dynamic operators on semi‐infinite time scale are studied in the Hilbert space , that the extensions of a minimal symmetric operator in limit‐point case. We construct a self‐adjoint dilation of the dissipative operator together with its incoming and outgoing spectral representations so that we can determine the scattering function of the dilation as stated in the scheme of Lax‐Phillips. Moreover, we construct a functional model of the dissipative operator and identify its characteristic function in terms of the Weyl‐Titchmarsh function of a self‐adjoint second‐order dynamic operator. Finally, we prove the theorems on completeness of the system of root functions of the dissipative and accumulative dynamic operators. 相似文献
44.
In this paper, an unstable linear time invariant (LTI) ODE system is stabilized exponentially by the PDE compensato—a wave equation with Kelvin‐Voigt (K‐V) damping. Direct feedback connections between the ODE system and wave equation are established: The velocity of the wave equation enters the ODE through the variable vt(1,t); meanwhile, the output of the ODE is fluxed into the wave equation. It is found that the spectrum of the system operator is composed of two parts: point spectrum and continuous spectrum. The continuous spectrum consists of an isolated point , and there are two branches of asymptotic eigenvalues: the first branch approaches to , and the other branch tends to ?∞. It is shown that there is a sequence of generalized eigenfunctions, which forms a Riesz basis for the Hilbert state space. As a consequence, the spectrum‐determined growth condition and exponential stability of the system are concluded. 相似文献
45.
ABSTRACTA class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays. 相似文献
46.
本文针对求矩阵方程AXB+CXD=F唯一解的参数迭代法,分析当矩阵A,B,C,D均是Hermite正(负)定矩阵时,迭代矩阵的特征值表达式,给出了最优参数的确定方法,并提出了相应的加速算法. 相似文献
47.
The new DP AdSV method for high sensitive Fe(III) determination in the presence of Solochrome Violet RS was developed. The use of an innovative renewable amalgam film electrode Hg(Ag)FE allowed to obtain high sensitivity and significantly minimize the mercury consumption. The best results were obtained for surface area of Hg(Ag)FE equal to 11.8 mm2. Instrumental parameters were optimized. The optimal results were obtained using differential pulse technique for the following values: sampling and waiting time ts=tw=10 ms, step potential Es=5 mV, pulse amplitude ΔE=50 mV. Measurements were conducted in 0.05 M acetate buffer (pH 5.6), the concentration of SVRS was equal to 5 μM. Deposition step was carried out at the potential ?400 mV for 20 s. Calculated detection limit for 40 s preconcentration time was equal to 1.4 nM (78 ng L?1). The influence of the common in environment, organic and inorganic interferences was studied. The developed method for Fe(III) determination was successfully applied and validated by investigation of certified reference material SPS‐SW2 Batch 118 and recovery of Fe(III) from various spiked samples as snow, tap water and bottom sediments. The repeatability (for 50 nM of Fe(III)) of the developed method expressed as CV was equal 3.1 % (n=5). 相似文献
48.
Benjamin Arras Ehsan Azmoodeh Guillaume Poly Yvik Swan 《Stochastic Processes and their Applications》2019,129(7):2341-2375
We provide a bound on a distance between finitely supported elements and general elements of the unit sphere of . We use this bound to estimate the Wasserstein-2 distance between random variables represented by linear combinations of independent random variables. Our results are expressed in terms of a discrepancy measure related to Nourdin–Peccati’s Malliavin–Stein method. The main application is towards the computation of quantitative rates of convergence to elements of the second Wiener chaos. In particular, we explicit these rates for non-central asymptotic of sequences of quadratic forms and the behavior of the generalized Rosenblatt process at extreme critical exponent. 相似文献
49.
50.
Émeline Schmisser 《Stochastic Processes and their Applications》2019,129(12):5364-5405
In this article, we consider a jump diffusion process , with drift function , diffusion coefficient and jump coefficient . This process is observed at discrete times . The sampling interval tends to 0 and the time interval tends to infinity. We assume that is ergodic, strictly stationary and exponentially -mixing. We use a penalized least-square approach to compute adaptive estimators of the functions and . We provide bounds for the risks of the two estimators. 相似文献