共查询到20条相似文献,搜索用时 15 毫秒
1.
The transition mechanism of jump processes between two different subsets in state space reveals important dynamical information of the processes and therefore has attracted considerable attention in the past years. In this paper, we study the first passage path ensemble of both discrete-time and continuous-time jump processes on a finite state space. The main approach is to divide each first passage path into nonreactive and reactive segments and to study them separately. The analysis can be applied to jump processes which are non-ergodic, as well as continuous-time jump processes where the waiting time distributions are non-exponential. In the particular case that the jump processes are both Markovian and ergodic, our analysis elucidates the relations between the study of the first passage paths and the study of the transition paths in transition path theory. We provide algorithms to numerically compute statistics of the first passage path ensemble. The computational complexity of these algorithms scales with the complexity of solving a linear system, for which efficient methods are available. Several examples demonstrate the wide applicability of the derived results across research areas. 相似文献
2.
We compute the Hamiltonian and Lagrangian associated to the large deviations of the trajectory of the empirical distribution for independent Markov processes, and of the empirical measure for translation invariant interacting Markov processes. We treat both the case of jump processes (continuous-time Markov chains and interacting particle systems) as well as diffusion processes. For diffusion processes, the Lagrangian is a quadratic form of the deviation of the trajectory from the solution of the Kolmogorov forward equation. In all cases, the Lagrangian can be interpreted as a relative entropy or relative entropy density per unit time. 相似文献
3.
In this paper we propose a model of electricity market based on the forward rate dynamics described by a diffusion with jumps as a generalization of the classical diffusion approach. We consider jump components resulting from a coupled continuous-time random walk (CTRW) with jump lengths proportional to the corresponding inter-jump time intervals. In the framework of the model we derive a formula for the EURO-price of a standard European call option, showing applicability of CTRW processes for pricing of financial instruments. The result, obtained by an advance theory of semimartingales, is an essential extension of the pricing formula derived in the classical diffusion model of the forward rate dynamics. It indicates an influence of both, the continuous and the jump parts of the forward rate process on the option price. 相似文献
4.
Our aim in this paper is to show how a probabilistic interpretation of the Boltzmann and Landau equations gives a microscopic understanding of these equations. We firstly associate stochastic jump processes with the Boltzmann equations we consider. Then we renormalize these equations following asymptotics which make prevail the grazing collisions, and prove the convergence of the associated Boltzmann jump processes to a diffusion process related to the Landau equation. The convergence is pathwise and also implies a convergence at the level of the partial differential equations. The best feature of this approach is the microscopic understanding of the transition between the Boltzmann and the Landau equations, by an accumulation of very small jumps. We deduce from this interpretation an approximation result for a solution of the Landau equation via colliding stochastic particle systems. This result leads to a Monte-Carlo algorithm for the simulation of solutions by a conservative particle method which enables to observe the transition from Boltzmann to Landau equations. Numerical results are given. 相似文献
5.
Coupled continuous time random walks (CTRWs) model normal and anomalous diffusion of random walkers by taking the sum of random jump lengths dependent on the random waiting times immediately preceding each jump. They are used to simulate diffusion-like processes in econophysics such as stock market fluctuations, where jumps represent financial market microstructure like log returns. In this and many other applications, the magnitude of the largest observations (e.g. a stock market crash) is of considerable importance in quantifying risk. We use a stochastic process called a coupled continuous time random maxima (CTRM) to determine the density governing the maximum jump length of a particle undergoing a CTRW. CTRM are similar to continuous time random walks but track maxima instead of sums. The many ways in which observations can depend on waiting times can produce an equally large number of CTRM governing density shapes. We compare densities governing coupled CTRM with their uncoupled counterparts for three simple observation/wait dependence structures. 相似文献
6.
We introduce a new formalism for computing the moments of transition events for nonhomogeneous Markov jump processes. Our method is applied directly to the master equation and does not involve the use of diffusion approximation. The general theory is applied to produce exact expressions for means and dispersions. For time homogeneous Markov processes with a finite number of connected states we are able to prove that both means and dispersions asymptotically increase linearly in time. 相似文献
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We introduce a class of facilitated asymmetric exclusion processes in which particles are pushed by neighbors from behind. For the simplest version in which a particle can hop to its vacant right neighbor only if its left neighbor is occupied, we determine the steady-state current and the distribution of cluster sizes on a ring. We show that an initial density downstep develops into a rarefaction wave that can have a jump discontinuity at the leading edge, while an upstep results in a shock wave. This unexpected rarefaction wave discontinuity occurs generally for facilitated exclusion processes. 相似文献
9.
L. Z.J. Liang D. Lemmens J. Tempere 《The European Physical Journal B - Condensed Matter and Complex Systems》2010,75(3):335-342
Path integral techniques for the pricing of financial options are mostly based on models that can be recast in terms of a
Fokker-Planck differential equation and that, consequently, neglect jumps and only describe drift and diffusion. We present
a method to adapt formulas for both the path-integral propagators and the option prices themselves, so that jump processes
are taken into account in conjunction with the usual drift and diffusion terms. In particular, we focus on stochastic volatility
models, such as the exponential Vasicek model, and extend the pricing formulas and propagator of this model to incorporate
jump diffusion with a given jump size distribution. This model is of importance to include non-Gaussian fluctuations beyond
the Black-Scholes model, and moreover yields a lognormal distribution of the volatilities, in agreement with results from
superstatistical analysis. The results obtained in the present formalism are checked with Monte Carlo simulations. 相似文献
10.
Atomic jumps in icosahedral (AlCu)Li quasicrystals and related structures have been studied by molecular dynamics simulations.
In quasicrystalline structures jumps exists with jump vectors much shorter than an average nearest neighbor distance. This
is a consequence of the phasonic degree of freedom. The jumps therefore are called flips and the sites connected by the jump
vector are denoted alternative positions. We find that the atoms in the quasicrystal structures studied here do not flip to
alternative positions as proposed and observed in decagonal or dodecagonal quasicrystals but jump to sites which are at least
an ordinary interatomic distance apart. Furthermore we observe two diffusion regimes: below about 55% of the melting temperature
only small (AlCu) atoms carry out ring processes whereas at higher temperatures both kinds of atoms contribute to long-range
diffusion.
Received 21 July 1999 相似文献
11.
We study the dissipative, classical dynamics of a charged particle in the presence of a magnetic field. Two stochastic models
are employed, and a comparative analysis is made, one based on diffusion processes and the other on jump processes. In the
literature on collision-broadening of spectral lines, these processes go under the epithet of weak-collision model and Boltzmann-Lorentz
model, respectively. We apply our model calculation to investigate the effect of magnetic field on the collision-broadened
spectral lines, when the emitter carries an electrical charge. The spectral lines show narrowing as the magnetic field is
increased, the narrowing being sharper in the Boltzmann-Lorentz model than in the weak collision model. 相似文献
12.
V. M. Tsvetkov A. A. Pikulev E. A. Sosnin S. M. Avdeev V. F. Tarasenko 《Technical Physics》2010,55(6):807-811
Data for the pressure jump are used to study thermodynamic processes in barrier-discharge excilamps under the conditions of
a diffuse (uniform) discharge and microdischarges. It is shown that a linear relationship between the pressure jump and excilamp
radiation intensity can help to control the radiation power. 相似文献
13.
We report the results of an experimental investigation of the mechanics and transport processes at the bounding interface between the turbulent and nonturbulent regions of flow in a turbulent jet, which shows the existence of a finite jump in the tangential velocity at the interface. This is associated with small-scale eddying motion at the outward propagating interface (nibbling) by which irrotational fluid becomes turbulent, and this implies that large-scale engulfment is not the dominant entrainment process. Interpretation of the jump as a singular structure yields an essential and significant contribution to the mean shear in the jet mixing region. Finally, our observations provide a justification for Prandtl's original hypothesis of a constant eddy viscosity in the nonturbulent outer jet region. 相似文献
14.
We study a model for microscopic segregation in a
homogeneous system of particles moving on a one-dimensional
lattice. Particles tend to separate from each other, and evolution
ceases when at least one empty site is found between any two
particles. Motion is a mixture of diffusion to nearest-neighbour
sites and long-range jumps, known as annealed small-world
propagation. The long-range jump probability plays the role of
the small-world disorder. We show that there is an optimal value
of this probability, for which the segregation process is
fastest. Moreover, above a critical probability, the time needed
to reach a fully segregated state diverges for asymptotically
large systems. These special values of the long-range jump
probability depend crucially on the particle density. Our system
is a novel example of the rare dynamical processes with critical
behaviour at a finite value of the small-world disorder. 相似文献
15.
The Laplace distribution of random processes was observed in numerous situations that include glasses, colloidal suspensions, live cells, and firm growth. Its origin is not so trivial as in the case of Gaussian distribution, supported by the central limit theorem. Sums of Laplace distributed random variables are not Laplace distributed. We discovered a new mechanism leading to the Laplace distribution of observable values. This mechanism changes the contribution ratio between a jump and a continuous parts of random processes. Our concept uses properties of Bernstein functions and subordinators connected with them. 相似文献
16.
Discrete-time random walks simulate diffusion if the single-step probability density function (jump distribution) generating the walk is sufficiently shortranged. In contrast, walks with long-ranged jump distributions considered in this paper simulate Lévy or stable processes. A one-dimensional walk with a selfsimilar jump distribution (the Weierstrass random walk) and its higherdimensional generalizations generate fractal trajectories if certain transience criteria are met and lead to simple analogs of deep results on the Hausdorff-Besicovitch dimension of stable processes. The Weierstrass random walk is lacunary (has gaps in the set of allowed steps) and its characteristic function is Weierstrass' non-differentiable function. Other lacunary random walks with characteristic functions related to Riemann's zeta function and certain numbertheoretic functions have very interesting analytic structure. 相似文献
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We evaluate the scale at which the multifractal structure of some random Gibbs measures becomes discernible. The value of this scale is obtained through what we call the growth speed in Hölder singularity sets of a Borel measure. This growth speed yields new information on the multifractal behavior of the rescaled copies involved in the structure of statistically self-similar Gibbs measures. Our results are useful to understand the multifractal nature of various heterogeneous jump processes. 相似文献