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191.
This paper deals with the boundedness in probability and convergence for solutions of stochastic Liénard-type equations. Some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained. We also show that white noise can affect the boundedness of corresponding deterministic Liénard equations. 相似文献
192.
Herbert Spohn 《Journal of statistical physics》1990,59(5-6):1227-1239
It has been proved that a tracer particle in a reversible lattice gas converges to Brownian motion. However, only in a few particular cases has a strictly positive self-diffusion coefficientD been established. Here we supply the missing piece and show thatD>0 in general. The exceptions are one-dimensional lattice gases with nearest neighbor jumps only, for whichD=0. The proof establishes a variational formula forD which could be used to obtain realistic bounds. 相似文献
193.
In this article, authors begin with establishing representation formulas and properties for functions on Carnot groups. Then, some unique continuation results to solutions of sub-Laplace equations with potentials are proved. 相似文献
194.
Akihiro Tohsaki 《Frontiers of Physics》2011,6(3):320-336
We explain how to treat a microscopic wave function of ??-condensation taking a 3??-nucleus as a typical example. The wave function has been originally proposed ten years before by Horiuchi, R?pke, Schuck and the present author (Phys. Rev. Lett., 2001, 87: 192501). The microscopic model, which fully takes into account the Pauli principle between all the constituent nucleons, effective internucleon forces and the Coulomb force, can play an important role in reproducing an ??-gas nature thanks to ??-condensation as an excited state of ??-like nuclei. An essential point of the wave function is to describe their ground state simultaneously. We study its typical features by giving an analytical formula of the norm kernel and the kernel concerning the one-body operator for 3??-condensation. 相似文献
195.
This note contains a generalization of the Trotter product formula to the setting of multiple linear systems of stochastic differential equations. From the result it follows that the solution of a system in Stratonovich form in a Lie algebra lies in the corresponding Lie group 相似文献
196.
We derive a change of variable formula for non-anticipative functionals defined on the space of Rd-valued right-continuous paths with left limits. The functionals are only required to possess certain directional derivatives, which may be computed pathwise. Our results lead to functional extensions of the Itô formula for a large class of stochastic processes, including semimartingales and Dirichlet processes. In particular, we show the stability of the class of semimartingales under certain functional transformations. 相似文献
197.
We settle a conjecture of Joseph Renes about the existence and construction of certain equiangular tight frames. 相似文献
198.
We give a Newton type rational interpolation formula (Theorem 2.2). It contains as a special case the original Newton interpolation, as well as the interpolation formula of Liu, which allows to recover many important classical q-series identities. We show in particular that some bibasic identities are a consequence of our formula. 相似文献
199.
B. S. Goh 《Journal of Optimization Theory and Applications》2009,142(2):275-289
We show that, for an unconstrained optimization problem, the long-term optimal trajectory consists of a sequence of greatest
descent directions and a Newton method in the final iteration. The greatest descent direction can be computed approximately
by using a Levenberg-Marquardt like formula. This implies the view that the Newton method approximates a Levenberg-Marquardt
like formula at a finite distance from the minimum point, instead of the standard view that the Levenberg-Marquadt formula
is a way to approximate the Newton method. With the insight gained from this analysis, we develop a two-dimensional version
of a Levenberg-Marquardt like formula. We make use of the two numerically largest components of the gradient vector to define
here new search directions. In this way, we avoid the need of inverting a high-dimensional matrix. This reduces also the storage
requirements for the full Hessian matrix in problems with a large number of variables.
The author thanks Mark Wu, Professors Sanyang Liu, Junmin Li, Shuisheng Zhou and Feng Ye for support and help in this research
as well as the referees for helpful comments. 相似文献
200.