1,074 research outputs found
A Class of Mean-field LQG Games with Partial Information
The large-population system consists of considerable small agents whose
individual behavior and mass effect are interrelated via their state-average.
The mean-field game provides an efficient way to get the decentralized
strategies of large-population system when studying its dynamic optimizations.
Unlike other large-population literature, this current paper possesses the
following distinctive features. First, our setting includes the partial
information structure of large-population system which is practical from real
application standpoint. Specially, two cases of partial information structure
are considered here: the partial filtration case (see Section 2, 3) where the
available information to agents is the filtration generated by an observable
component of underlying Brownian motion; the noisy observation case (Section 4)
where the individual agent can access an additive white-noise observation on
its own state. Also, it is new in filtering modeling that our sensor function
may depend on the state-average. Second, in both cases, the limiting
state-averages become random and the filtering equations to individual state
should be formalized to get the decentralized strategies. Moreover, it is also
new that the limit average of state filters should be analyzed here. This makes
our analysis very different to the full information arguments of
large-population system. Third, the consistency conditions are equivalent to
the wellposedness of some Riccati equations, and do not involve the fixed-point
analysis as in other mean-field games. The -Nash equilibrium
properties are also presented.Comment: 19 page
Regularity properties for general HJB equations. A BSDE method
In this work we investigate regularity properties of a large class of
Hamilton-Jacobi-Bellman (HJB) equations with or without obstacles, which can be
stochastically interpreted in form of a stochastic control system which
nonlinear cost functional is defined with the help of a backward stochastic
differential equation (BSDE) or a reflected BSDE (RBSDE). More precisely, we
prove that, firstly, the unique viscosity solution of such a HJB
equation over the time interval with or without an obstacle, and with
terminal condition at time , is jointly Lipschitz in , for
running any compact subinterval of . Secondly, for the case that
solves a HJB equation without an obstacle or with an upper obstacle it is shown
under appropriate assumptions that is jointly semiconcave in .
These results extend earlier ones by Buckdahn, Cannarsa and Quincampoix [1].
Our approach embeds their idea of time change into a BSDE analysis. We also
provide an elementary counter-example which shows that, in general, for the
case that solves a HJB equation with a lower obstacle the semi-concavity
doesn't hold true.Comment: 30 page
Necessary Condition for Near Optimal Control of Linear Forward-backward Stochastic Differential Equations
This paper investigates the near optimal control for a kind of linear
stochastic control systems governed by the forward backward stochastic
differential equations, where both the drift and diffusion terms are allowed to
depend on controls and the control domain is not assumed to be convex. In the
previous work (Theorem 3.1) of the second and third authors [\textit{%
Automatica} \textbf{46} (2010) 397-404], some problem of near optimal control
with the control dependent diffusion is addressed and our current paper can be
viewed as some direct response to it. The necessary condition of the
near-optimality is established within the framework of optimality variational
principle developed by Yong [\textit{SIAM J. Control Optim.} \textbf{48} (2010)
4119--4156] and obtained by the convergence technique to treat the optimal
control of FBSDEs in unbounded control domains by Wu [% \textit{Automatica}
\textbf{49} (2013) 1473--1480]. Some new estimates are given here to handle the
near optimality. In addition, an illustrating example is discussed as well.Comment: To appear in International Journal of Contro
A Linear-Quadratic Optimal Control Problem for Mean-Field Stochastic Differential Equations in Infinite Horizon
A linear-quadratic (LQ, for short) optimal control problem is considered for
mean-field stochastic differential equations with constant coefficients in an
infinite horizon. The stabilizability of the control system is studied followed
by the discussion of the well-posedness of the LQ problem. The optimal control
can be expressed as a linear state feedback involving the state and its mean,
through the solutions of two algebraic Riccati equations. The solvability of
such kind of Riccati equations is investigated by means of semi-definite
programming method.Comment: 40 page
Pricing Strategy for Cloud Computing Services
The cloud services market exhibits unique characteristics such as instant accessibility, fluctuating demand and supply, and interruptible service provision. Various pricing mechanisms exist in current industry practice, however, none is comprehensive enough to capture all these features. In my work, I identify key factors related to cloud computing pricing. My dissertation includes three essays. They employ multiple approaches, including market survey, game theory modelling, simulation, lab experiments and econometric modelling, to analyse the pricing strategy of cloud services vendors. The first essay highlights nine important factors in current cloud pricing practice and proposes three missing factors based on a market survey. In the second essay, I build an analytical model and use simulation to derive optimal pricing strategies for a monopoly cloud services vendor that operates in the reserved services market and the spot services market. In the last piece of work, I examine the client’s willingness-to-pay for customized cloud services through behavioural experiments
Topological responses from chiral anomaly in multi-Weyl semimetals
Multi-Weyl semimetals are a kind of topological phase of matter with discrete
Weyl nodes characterized by multiple monopole charges, in which the chiral
anomaly, the anomalous nonconservation of an axial current, occurs in the
presence of electric and magnetic fields. Electronic transport properties
related to the chiral anomaly in the presence of both electromagnetic fields
and axial electromagnetic fields in multi-Weyl semimetals are systematically
studied. It has been found that the anomalous Hall conductivity has a
modification linear in the axial vector potential from inhomogeneous strains.
The axial electric field leads to an axial Hall current that is proportional to
the distance of Weyl nodes in momentum space. This axial current may generate
chirality accumulation of Weyl fermions through delicately engineering the
axial electromagnetic fields even in the absence of external electromagnetic
fields. Therefore, this work provides a nonmagnetic mechanism of generation of
chirality accumulation in Weyl semimetals and might shed new light on the
application of Weyl semimetals in the emerging field of valleytronics.Comment: 13 pages, 2 tables, 2 figures, accepted by Physical Review
Renormalization Group Approach to Stability of Two-dimensional Interacting Type-II Dirac Fermions
The type-II Weyl/Dirac fermions are a generalization of conventional or
type-I Weyl/Dirac fermions, whose conic spectrum is tilted such that the Fermi
surface becomes lines in two dimensions, and surface in three dimensions rather
than discrete points of the conventional Weyl/Dirac fermions. The
mass-independent renormalization group calculations show that the tilting
parameter decreases monotonically with respect to the length scale, which leads
to a transition from two dimensional type-II Weyl/Dirac fermions to the type-I
ones. Because of the non-trivial Fermi surface, a photon gains a finite mass
partially via the chiral anomaly, leading to the strong screening effect of the
Weyl/Dirac fermions. Consequently, anisotropic type-II Dirac semimetals become
stable against the Coulomb interaction. This work provides deep insight into
the interplay between the geometry of Fermi surface and the Coulomb
interaction.Comment: Final pulished versio
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