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151.
Let t be a continuous Markov chain on N states. Consider adjoining a Brownian motion with this Markov chain so that the drift and the variance take different values when t is in different states. This new process Zt is a hidden Markov process. We study the probability distribution of the first passage time for Zt.Our result, when applied to the stock market, provides an explicit mathematical interpretation of the fact that in finite time, there is positive probability for the bull (bear) market to become bear (bull). 相似文献
152.
Sergei V. Zubov 《Southeast Asian Bulletin of Mathematics》2000,24(1):155-172
Consider a new concept of stability of the so-called rated motion of a system of an ordinary differential equations. A rated motion need not be a solution of this system at all. In terms of Lyapunovs direct method, formulate and prove certain statements about rated stability, asymptotically rated stability, and rated unstability of zero motion of a system of an ordinary differential equations.AMS Subject Classification (1991): 34D05 34D35 93D30 93D20 相似文献
153.
More on P-Stable Convex Sets in Banach Spaces 总被引:2,自引:0,他引:2
We study the asymptotic behavior and limit distributions for sums S
n =bn
-1 i=1
n i,where
i, i 1, are i.i.d. random convex compact (cc) sets in a given separable Banach space B and summation is defined in a sense of Minkowski. The following results are obtained: (i) Series (LePage type) and Poisson integral representations of random stable cc sets in B are established; (ii) The invariance principle for processes S
n(t) =bn
-1 i=1
[nt] i, t[0, 1], and the existence of p-stable cc Levy motion are proved; (iii) In the case, where
i are segments, the limit of S
n is proved to be countable zonotope. Furthermore, if B = R
d
, the singularity of distributions of two countable zonotopes Yp
1, 1,Yp
2, 2, corresponding to values of exponents p
1, p
2 and spectral measures
1,
2, is proved if either p
1 p
2 or
1
2; (iv) Some new simple estimates of parameters of stable laws in R
d
, based on these results are suggested. 相似文献
154.
Hrvoje Šikić 《Journal of Theoretical Probability》2000,13(2):571-574
We prove that for a>0, (B
t) one-dimensional standard Brownian motion and
0=inf{t>0 : B
t=0} the following zero–one law is valid
相似文献
155.
In order to understand the rise of runaway solutions in the radiation reaction problem a mechanical model is used. An alternative
demonstration of Daboul’s theorem, through Hurwitz’s criterion, is given. The origin of runaway solutions in electrodynamics
is discussed. They arise when the particle has a negative mechanical mass or when approximations are used in the equation
of motion. In the 1-dimensional mechanical model an exact and linear equation of motion for the particle is obtained, the
corresponding exact solution is again runaway when the mechanical mass is negative. The exact solution is not runaway when
the mechanical mass is positive. However, the use of approximations leads to an equation of motion which has runaway solutions.
It is exhibited that the use of approximations in the 3-dimensional mechanical model is completely necessary because the general
equation of motion for the particle is non-linear. The analysis of this case proceeds in a very similar way to the one carried
out in electrodynamics. This means that the number of dimensions also plays an important role in the analysis. 相似文献
156.
We proposed in this study a novel analog complementary metal oxide semiconductor (CMOS) circuit for generating a motion signal
when an object moves, which is a simple structure. The proposed unit circuit was constructed using a previously proposed edge
detection circuit and a novel proposed circuit for generating a motion signal which accepts an edge signal. The part for generating
the motion signal was constructed using six metal oxide semiconductor (MOS) transistors and one capacitor. Results obtained
by the simulation program with integrated circuit emphasis (SPICE) and the measured results of a test circuit constructed
with discrete MOS transistors and the test circuit fabricated with a 1.2 μm CMOS process showed that the proposed unit circuit
can output pulsed current (motion signal) when an object moves on the circuit. It was clarified from the SPICE results that
the two-dimensional network constructed with proposed unit circuits can output motion signals. The size of the novel unit
circuit is expected to be about 110 × 110μm2 obtained by the 1.2 μm CMOS process. It is possible to arrange 90 × 90 unit circuits on a chip which has an area of 1 × 1cm2. The aperture ratio is expected to be about 21%, which is twice as large as that of the previously proposed circuit. An integrated
circuit for image processing in real time can thus be realized by applying the two-dimensional network constructed with the
proposed circuits. 相似文献
157.
Björn Birnir 《Journal of statistical physics》2007,128(1-2):535-568
A system of ordinary differential equations (ODEs) is derived from a discrete system of Vicsek, Czirók et al. [Phys. Rev. Lett.
75(6):1226–1229, 1995], describing the motion of a school of fish. Classes of linear and stationary solutions of the ODEs are
found and their stability explored using equivariant bifurcation theory. The existence of periodic and toroidal solutions
is also proven under deterministic perturbations and structurally stable heteroclinic connections are found. Applications
of the model to the migration of the capelin, a pelagic fish that undertakes an extensive migration in the North Atlantic,
are discussed and simulation of the ODEs presented. 相似文献
158.
E. Scalas U. Garibaldi S. Donadio 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,60(2):271-272
This erratum corrects a mistake in reference [E. Scalas, U. Garibaldi, S. Donadio, Eur. Phys. J. B 53, 267 (2006)].
In that paper,
we needed an aperiodic version of the BDY game, but, in formula (1),
we incorrectly presented
a periodic transition matrix of period 2 in the special case of g = 2 agents.
Here, we present the right aperiodic version. 相似文献
159.
B. Dybiec L. Schimansky-Geier 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,57(3):313-320
We study the stationary probability density of a Brownian particle in a potential with a single-well subject to the purely
additive thermal and dichotomous noise sources. We find situations where bimodality of stationary densities emerges due to
presence of dichotomous noise. The solutions are constructed using stochastic dynamics (Langevin equation) or by discretization
of the corresponding Fokker-Planck equations. We find that in models with both noises being additive the potential has to
grow faster than |x| in order to obtain bimodality. For potentials ∝|x| stationary solutions are always of the double exponential
form. 相似文献
160.