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Maximal inequalities and space-time regularity of stochastic convolutions

Szymon Peszat, Jan Seidler (1998)

Mathematica Bohemica

Space-time regularity of stochastic convolution integrals J = 0 S(-r)Z(r)W(r) driven by a cylindrical Wiener process W in an L 2 -space on a bounded domain is investigated. The semigroup S is supposed to be given by the Green function of a 2 m -th order parabolic boundary value problem, and Z is a multiplication operator. Under fairly general assumptions, J is proved to be Holder continuous in time and space. The method yields maximal inequalities for stochastic convolutions in the space of continuous...

Maximal regularity for stochastic convolutions in L p spaces

Giuseppe Da Prato, Alessandra Lunardi (1998)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We prove an optimal L p regularity result for stochastic convolutions in certain Banach spaces. It is stated in terms of real interpolation spaces.

Maximal Weak-Type Inequality for Orthogonal Harmonic Functions and Martingales

Adam Osękowski (2013)

Bulletin of the Polish Academy of Sciences. Mathematics

Assume that u, v are conjugate harmonic functions on the unit disc of ℂ, normalized so that u(0) = v(0) = 0. Let u*, |v|* stand for the one- and two-sided Brownian maxima of u and v, respectively. The paper contains the proof of the sharp weak-type estimate ℙ(|v|* ≥ 1)≤ (1 + 1/3² + 1/5² + 1/7² + ...)/(1 - 1/3² + 1/5² - 1/7² + ...) 𝔼u*. Actually, this estimate is shown to be true in the more general setting of differentially subordinate harmonic functions defined...

Maximizing multi–information

Nihat Ay, Andreas Knauf (2006)

Kybernetika

Stochastic interdependence of a probability distribution on a product space is measured by its Kullback–Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed description of the structure of probability distributions with globally maximal multi-information we obtain our main result: The exponential family...

Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

Kuo-Hsiung Wang, Sheau-Chyi Chen, Jau-Chuan Ke (2004)

RAIRO - Operations Research - Recherche Opérationnelle

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability ( 1 - b ) . We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter ρ , the...

Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

Kuo-Hsiung Wang, Sheau-Chyi Chen, Jau-Chuan Ke (2010)

RAIRO - Operations Research

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability (1 - b). We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter...

Maximum principle for forward-backward doubly stochastic control systems and applications

Liangquan Zhang, Yufeng Shi (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an example...

Maximum principle for forward-backward doubly stochastic control systems and applications*

Liangquan Zhang, Yufeng Shi (2011)

ESAIM: Control, Optimisation and Calculus of Variations

The maximum principle for optimal control problems of fully coupled forward-backward doubly stochastic differential equations (FBDSDEs in short) in the global form is obtained, under the assumptions that the diffusion coefficients do not contain the control variable, but the control domain need not to be convex. We apply our stochastic maximum principle (SMP in short) to investigate the optimal control problems of a class of stochastic partial differential equations (SPDEs in short). And as an...

Maximum principle for optimal control of fully coupled forward-backward stochastic differential delayed equations

Jianhui Huang, Jingtao Shi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with the optimal control problem in which the controlled system is described by a fully coupled anticipated forward-backward stochastic differential delayed equation. The maximum principle for this problem is obtained under the assumption that the diffusion coefficient does not contain the control variables and the control domain is not necessarily convex. Both the necessary and sufficient conditions of optimality are proved. As illustrating examples, two kinds of linear quadratic...

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