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961.
This paper is concerned with the existence of an optimal control problem for a quasi-linear elliptic obstacle variational inequality in which the obstacle is taken as the control. Firstly, we get some existence results under the assumption of the leading operator of the variational inequality with a monotone type mapping in Section 2. In Section 3, as an application, without the assumption of the monotone type mapping for the leading operator of the variational inequality, we prove that the leading operator of the variational inequality is a monotone type mapping. Existence of the optimal obstacle is proved. The method used here is different from [Y.Y. Zhou, X.Q. Yang, K.L. Teo, The existence results for optimal control problems governed by a variational inequality, J. Math. Anal. Appl. 321 (2006) 595-608]. 相似文献
962.
963.
We propose and study a mutualism model with feedback controls. By applying a new differential inequality, we show that the conditions which ensure the permanence of the system are the same as that of the model without feedback controls, which means that the feedback control variables have no influence on the persistent property of the system. Our results not only improve but also complement some existing ones. 相似文献
964.
We consider stochastic equations in Hilbert spaces with singular drift in the framework of [G. Da Prato, M. Röckner, Singular dissipative stochastic equations in Hilbert spaces, Probab. Theory Related Fields 124 (2) (2002) 261-303]. We prove a Harnack inequality (in the sense of [F.-Y. Wang, Logarithmic Sobolev inequalities on noncompact Riemannian manifolds, Probab. Theory Related Fields 109 (1997) 417-424]) for its transition semigroup and exploit its consequences. In particular, we prove regularizing and ultraboundedness properties of the transition semigroup as well as that the corresponding Kolmogorov operator has at most one infinitesimally invariant measure μ (satisfying some mild integrability conditions). Finally, we prove existence of such a measure μ for noncontinuous drifts. 相似文献
965.
S. Furuichi K. Yanagi K. Kuriyama 《Journal of Mathematical Analysis and Applications》2009,356(1):179-1156
We introduce a generalized Wigner-Yanase skew information and then derive the trace inequality related to the uncertainty relation. This inequality is a non-trivial generalization of the uncertainty relation derived by S. Luo for the quantum uncertainty quantity excluding the classical mixture. In addition, several trace inequalities on our generalized Wigner-Yanase skew information are argued. 相似文献
966.
Let X be a space of homogeneous type in the sense of Coifman and Weiss. In this paper, via a new Cotlar type inequality linking commutators and corresponding maximal operators, a weighted Lp(X) estimate with general weights and a weak type endpoint estimate with A1(X) weights are established for maximal operators corresponding to commutators of BMO(X) functions and singular integral operators with non-smooth kernels. 相似文献
967.
Emmanuel Rio 《Journal of Theoretical Probability》2009,22(1):146-163
We obtain precise constants in the Marcinkiewicz-Zygmund inequality for martingales in
for p>2 and a new Rosenthal type inequality for stationary martingale differences for p in ]2,3]. The Rosenthal inequality is then extended to stationary and adapted sequences. As in Peligrad et al. (Proc. Am.
Math. Soc. 135:541–550, [2007]), the bounds are expressed in terms of
-norms of conditional expectations with respect to an increasing field of sigma algebras. Some applications to a particular
Markov chain are given.
相似文献
968.
Rasul A. Khan 《Journal of Theoretical Probability》2009,22(2):348-364
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
相似文献
969.
Mark Veraar 《Potential Analysis》2009,30(4):341-370
In this paper we extend certain correlation inequalities for vector-valued Gaussian random variables due to Kolmogorov and Rozanov. The inequalities are applied to sequences of Gaussian random variables and Gaussian processes. For sequences of Gaussian random variables satisfying a correlation assumption, we prove a Borel-Cantelli lemma, maximal inequalities and several laws of large numbers. This extends results of Be?ka and Ciesielski and of Hytönen and the author. In the second part of the paper we consider a certain class of vector-valued Gaussian processes which are α-Hölder continuous in p-th moment. For these processes we obtain Besov regularity of the paths of order α. We also obtain estimates for the moments in the Besov norm. In particular, the results are applied to vector-valued fractional Brownian motions. These results extend earlier work of Ciesielski, Kerkyacharian and Roynette and of Hytönen and the author. 相似文献
970.
在Banach空间中引入了一类广义F-互补问题,研究了它与一类变分不等式问题的等价性关系,给出了此类变分不等式问题的解的存在唯一性定理. 相似文献