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1.
In statistical physics, anomalous diffusion plays an important role, whose applications have been found in many areas. In this paper, we introduce a composite-diffusive fractional Brownian motion X α,H (t)=X H (S α (t)), 0<α,H<1, driven by anomalous diffusions as a model of asset prices and discuss the corresponding fractional Fokker-Planck equation and Black-Scholes formula. We obtain the fractional Fokker-Planck equation governing the dynamics of the probability density function of the composite-diffusive fractional Brownian motion and find the Black-Scholes differential equation driven by the stock asset X α,H (t) and the corresponding Black-Scholes formula for the fair prices of European option.  相似文献   

2.
The time- and temperature-dependent drift mobility μd for dispersive transients in disordered solids is μd(T,t) = LEtT in terms of distance L, field E and transit time tT. Since current Itsu?(1?α) for t <Tand 0<α<1 by Scher-Montroll theory for hopping among localized states, it follows that μd(T) = α[μd(T,t)]α (L)1?α where τ≈ 10?13s is estimated. Further μd(T) ∝ exp (0KT) and the activation energy Δ0 is time independent. On this basis Δ for the carbazole polymers is ca. zero, that for a-Se is ca. 0.05 eV, and that for a-As2Se3 is 0.35 eV rather than 0.5, 0.3 and 0.6 eV respectively on a phenomenological basis for μd(T,t). Trap-controlled hopping transport may be excluded. Time-resolved optical studies of excess carrier recombination supplement mobility measurements in a-Si:H and a-As2Se3 as well as other systems. Combined results suggest a dielectric response mechanism in which the time-dependent hopping frequency of localized carriers ν ∝ tα?1 arises from distortion of the medium at localization sites. This is satisfied by Δ(T,t) = Δ0+(1?α)KTT ln(t/τ) where τ is the mean initial localization time of the carrier, 10?13?10?12s, Δio is the height of the barrier at T, and 0<α<l. Consequently ν = ν0(t/τ)α?1 exp(frsol|?Δ0/KT) which applies also to bimolecular recombination.  相似文献   

3.
A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t0 where A(s, t) is the absorptive part of the elastic scattering amplitude and t0 is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like sα(t)lnη(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t0, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.  相似文献   

4.
A model for option pricing of fractional version of the Merton model with ‘Hurst exponent’ H being in [1/2,1) is established with transaction costs. In particular, for H(1/2,1) the minimal price Cmin(t,St) of an option under transaction costs is obtained, which displays that the timestep δt and the ‘Hurst exponent’ H play an important role in option pricing with transaction costs.  相似文献   

5.
Natural lifetimes of some highly excited levels in the Pb-I spectrum have been measured by the zero field level crossing (Hanle) method. The levels were reached by optical excitation from the metastable 6p 2 3 P 2 and 6p 2 3 P 1 states, were a considerable population had been created by means of adc discharge in a Pb atomic beam. An atomic beam source producing atoms in metastable states is described. For the lifetimes τ of the investigated levels we find:τ(6p(1/2)6d 3 D 1)=3.74(28) ns,τ(6p(1/2)6d 3 F 2)=25.8(1.3) ns,τ(6p(1/2)6d 3 D 2)=4.17(?31) (?49) ns,τ(6p(1/2)6d 3 F 3)=6.08(26) ns,τ(6p(3/2)7s)3 P 2=5.85(27) ns. These results are compared with lifetimes derived from oscillator strengths given in the literature.  相似文献   

6.
In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τN0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ0N, is normally given a value of 10−9 s, but values ranging from 10−8 to 10−12 s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).  相似文献   

7.
We measured the elastic scattering of αα ats = 126 GeV and of αp at s = 89 GeV. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV2. At small |t| = 0.05?0.07 GeV2, this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section αtot(αα) = 250 ± 50 mb and an integrated elastic cross section σe1(αα) = 45 ± mb. Another method of estimating σtot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV2, and for 0.05 < |t| < 0.18 GeV2 behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σtot(αp) = 130 ± 20 and σe1(αp) = 20 ± 4mb. Results on pp elastic scattering at s = 63 GeV agree with previous ISR experiments.  相似文献   

8.
This paper deals with the problem of discrete-time option pricing by the mixed Brownian–fractional Brownian model with transaction costs. By a mean-self-financing delta hedging argument in a discrete-time setting, a European call option pricing formula is obtained. In particular, the minimal pricing cmin(t,st) of an option under transaction costs is obtained, which shows that timestep δt and Hurst exponent H play an important role in option pricing with transaction costs. In addition, we also show that there exists fundamental difference between the continuous-time trade and discrete-time trade and that continuous-time trade assumption will result in underestimating the value of a European call option.  相似文献   

9.
We present here some fundamental but yet underlooked features of the propagation of weak ultrashort pulses (with Δdτ << 1, where Δd is the Doppler width and τ is the pulse duration) in resonant atomic media. We show that the pulse area behaviour and the pulse spectrum at resonance are governed by the usual optical depth (α0L, where α0 is the absorption coefficient at resonance and L the length of the medium), whereas the pertinent parameter that governs the severity of the dispersion effects and the distortion of the pulse is the dispersion parameter edisp = (α0L)Δdτ that we introduce. Paradoxical effect such as distortionless propagation (e.g. edisp << 1) with vanishing pulse area (when α0L >> 1) can then explained within this formalism.  相似文献   

10.
Radiative lifetimes of some highly excited levels in Sr I were measured by zero-field level crossing technique. These levels have been populated using optical excitation starting from the metastable 4d 5s 1 D 2 or 5s5p 3 P 2,1,0 states. The high population of these metastable levels necessary for the experiments was obtained by a discharge in the pure Sr vapour burning in the atomic beam oven. The following lifetimes have been determined (in units of 10?8 sec):τ(5s 6s3 S 1)=1.09±0.11,τ(5s 5d 3D1)=1.67±0.10,τ(5s4f1 F 3)=3.43±0.28,τ(4d5p 1 D 2)=2.19±0.16,τ(5p 2 3P1)=0.88±0.12,τ(5p 2 3 P 2)=0.78 ?0.10 +0.26 . These results are compared with lifetimes derived from oscillator strengths given in the literature, and the reliability of different oscillator strengths tables is discussed. A corresponding discussion is given for radiative lifetimes of some levels in Ca I published previously. Good agreement with data derived from arc emission oscillator strengths has been found. Ca lifetimes are fairly well consistent with oscillator strengths calculated with semiempirical scaled Thomas-Fermi-wave functions.  相似文献   

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