6,040 research outputs found
Moment Boundedness of Linear Stochastic Delay Differential Equation with Distributed Delay
This paper studies the moment boundedness of solutions of linear stochastic
delay differential equations with distributed delay. For a linear stochastic
delay differential equation, the first moment stability is known to be
identical to that of the corresponding deterministic delay differential
equation. However, boundedness of the second moment is complicated and depends
on the stochastic terms. In this paper, the characteristic function of the
equation is obtained through techniques of Laplace transform. From the
characteristic equation, sufficient conditions for the second moment to be
bounded or unbounded are proposed.Comment: 38 pages, 2 figure
Efficient Data Gathering in Wireless Sensor Networks Based on Matrix Completion and Compressive Sensing
Gathering data in an energy efficient manner in wireless sensor networks is
an important design challenge. In wireless sensor networks, the readings of
sensors always exhibit intra-temporal and inter-spatial correlations.
Therefore, in this letter, we use low rank matrix completion theory to explore
the inter-spatial correlation and use compressive sensing theory to take
advantage of intra-temporal correlation. Our method, dubbed MCCS, can
significantly reduce the amount of data that each sensor must send through
network and to the sink, thus prolong the lifetime of the whole networks.
Experiments using real datasets demonstrate the feasibility and efficacy of our
MCCS method
How volatilities nonlocal in time affect the price dynamics in complex financial systems
What is the dominating mechanism of the price dynamics in financial systems
is of great interest to scientists. The problem whether and how volatilities
affect the price movement draws much attention. Although many efforts have been
made, it remains challenging. Physicists usually apply the concepts and methods
in statistical physics, such as temporal correlation functions, to study
financial dynamics. However, the usual volatility-return correlation function,
which is local in time, typically fluctuates around zero. Here we construct
dynamic observables nonlocal in time to explore the volatility-return
correlation, based on the empirical data of hundreds of individual stocks and
25 stock market indices in different countries. Strikingly, the correlation is
discovered to be non-zero, with an amplitude of a few percent and a duration of
over two weeks. This result provides compelling evidence that past volatilities
nonlocal in time affect future returns. Further, we introduce an agent-based
model with a novel mechanism, that is, the asymmetric trading preference in
volatile and stable markets, to understand the microscopic origin of the
volatility-return correlation nonlocal in time.Comment: 16 pages, 7 figure
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