نتایج جستجو برای: infinitesimal generators

تعداد نتایج: 27674  

Journal: :Communications of the American Mathematical Society 2023

We replace trees by multi-indices as an index set of the abstract model space to tackle quasi-linear singular stochastic partial differential equations. show that this approach is consistent with postulates regularity structures when it comes structure group, which arises from a Hopf algebra and comodule. Our approach, where dual naturally embeds into formal power series algebra, allows interpr...

2009
V. E. Tarasov

We propose a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators are infinitesimal generators of completely positive semigroups and describe the properties of this semigroup. We solve the proposed fractional quantum Mar...

2008
MICHAEL GEKHTMAN

Sato theory provides a correspondence between solutions to the KP hierarchy and points in an infinite dimensional Grassmannian. In this correspondence, flows generated infinitesimally by powers of the “shift” operator give time dependence to the first coordinate of an arbitrarily selected point, making it a tau-function. These tau-functions satisfy a number of integrable equations, including th...

1998
P. J. Fitzsimmons

Let X and Y be time-homogeneous Markov processes with common state space E, and assume that the transition kernels of X and Y admit densities with respect to suitable reference measures. We show that if there is a time t > 0 such that, for each x ∈ E, the conditional distribution of (Xs)0≤s≤t, given X0 = x = Xt, coincides with the conditional distribution of (Ys)0≤s≤t, given Y0 = x = Yt, then t...

2009
Peter J. Olver

Let G be a Lie group acting smoothly on a manifold M . A closed, nonsingular submanifold S ⊂M is called maximally symmetric if its symmetry subgroup GS ⊂ G has the maximal possible dimension, namely dimGS = dimS, and hence S = GS · z0 is an orbit of GS . Maximally symmetric submanifolds are characterized by the property that all their differential invariants are constant. In this paper, we expl...

Journal: :Int. J. Math. Mathematical Sciences 2005
M. S. Fofana

Whenever there is a time delay in a dynamical system, the study of stability becomes an infinite-dimensional problem. The centre manifold theorem, together with the classical Hopf bifurcation, is the most valuable approach for simplifying the infinite-dimensional problem without the assumption of small time delay. This dimensional reduction is illustrated in this paper with the delay versions o...

2012
Hongyang XU Yijun Zhu

In this paper, we investigate an M/M/c queue with single working vacations of partial servers and setup times. During the vacation period, some of which servers are not entirely stop the service but service the new customers at a lower service rate, the other servers have a normal vacation and stop the service. Quasi-birth-and-death-process and infinitesimal generators for the process are obtai...

2008
Ludger Rüschendorf

The aim of this paper is to unify and extend some of the various results on the ordering of option prices in exponential semimartingale models. This is a problem of interest not only for financial applications but similar questions also arise in the ordering properties of Markovian networks or in the problem to develop consistency results for risk measures for portfolio vectors with respect to ...

2016
Andrei Agrachev Ugo Boscain Robert Neel Luca Rizzi ANDREI AGRACHEV UGO BOSCAIN ROBERT NEEL

We relate some basic constructions of stochastic analysis to differential geometry, via random walk approximations. We consider walks on both Riemannian and sub-Riemannian manifolds in which the steps consist of travel along either geodesics or integral curves associated to orthonormal frames, and we give particular attention to walks where the choice of step is influenced by a volume on the ma...

2004
Boris Dubrovin Youjin Zhang

We prove that the extended Toda hierarchy of [1] admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m ≥ −1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau function of a generic solution to the extended Toda hierarchy is annihilated by a combination...

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