Related papers: On properties of Continuous-Time Random Walks with…
We study financial distributions within the framework of the continuous time random walk (CTRW). We review earlier approaches and present new results related to overnight effects as well as the generalization of the formalism which embodies…
Continuous-time random walk (CTRW) is a model of anomalous sub-diffusion in which particles are immobilized for random times between successive jumps. A power-law distribution of the waiting times, $\psi(\tau) \tau^{-(1+\alpha)}$, leads to…
Starting from a continuous time random walk (CTRW) model of particles that may evanesce as they walk, our goal is to arrive at macroscopic integro-differential equations for the probability density for a particle to be found at point r at…
We adapt continuous time random walk (CTRW) formalism to describe asset price evolution and discuss some of the problems that can be treated using this approach. We basically focus on two aspects: (i) the derivation of the price…
Initially developed in the framework of quantum stochastic calculus, the main equations of quantum stochastic filtering were later on derived as the limits of Markov models of discrete measurements under appropriate scaling. In many…
We consider the continuous time random walk model (CTRW) of tracer's motion in porous medium flows based on the experimentally determined distributions of pore velocity and pore size reported in Holzner et al. Phys. Rev. E 92, 013015…
Brownian motion is a well-known model for normal diffusion, but not all physical phenomena behave according to a Brownian motion. Many phenomena exhibit irregular diffusive behavior, called anomalous diffusion. Examples of anomalous…
The combined Continuous Time Random Walk (CTRW) in position and momentum space is introduced, in the form of two coupled integral equations that describe the evolution of the probability distribution for finding a particle at a certain…
We consider random variables observed at arrival times of a renewal process, which possibly depends on those observations and has regularly varying steps with infinite mean. Due to the dependence and heavy tailed steps, the limiting…
The continuous time random walk model plays an important role in modeling of so called anomalous diffusion behaviour. One of the specific property of such model are constant time periods visible in trajectory. In the continuous time random…
We show that for a weakly dense subset of the domain of attraction of a positive stable random variable of index $0<\alpha<1$($DOA\left(\alpha\right))$ the functional stable convergence is a time-changed renewal convergence of distribution…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
Recent findings suggest that processes such as the electronic energy transfer through the photosynthetic antenna display quantal features, aspects known from the dynamics of charge carriers along polymer backbones. Hence, in modeling energy…
Above two dimensions, diffusion of a particle in a medium with quenched random traps is believed to be well-described by the annealed continuous time random walk (CTRW). We propose an approximate expression for the first-passage-time (FPT)…
The continuous-time random walk (CTRW) is a pure-jump stochastic process with several applications in physics, but also in insurance, finance and economics. A definition is given for a class of stochastic integrals driven by a CTRW, that…
In this paper we continue our study of exit times for random walks with independent but not necessarily identical distributed increments. Our paper "First-passage times for random walks with non-identically distributed increments" was…
It is proved that the distributions of scaling limits of Continuous Time Random Walks (CTRWs) solve integro-differential equations akin to Fokker-Planck Equations for diffusion processes. In contrast to previous such results, it is not…
We show the asymptotic long-time equivalence of a generic power law waiting time distribution to the Mittag-Leffler waiting time distribution, characteristic for a time fractional CTRW. This asymptotic equivalence is effected by a…
Motivated by novel results in the theory of complex adaptive systems, we analyze the dynamics of random walks in which the jumping probabilities are {\it time-dependent}. We determine the survival probability in the presence of an absorbing…
Continuous time random Walk model has been versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as disordered or porous media. We are studying the continuous limits of Heterogeneous…