Tomasz Srokowski

  • Citations Per Year
Learn More
A jumping process, defined in terms of the Lévi distributed jumping size and the Poissonian, position-dependent waiting time with the algebraic jumping rate, is discussed on the assumption that parameters of both distributions are themselves random variables which are determined from given probability distributions. The fractional equation for the(More)
We present a stochastic jumping process, defined in terms of jump-size probability density and jumping rate, which is a generalization of the well-known kangaroo process. The definition takes into account two process values: after and before the jump. Therefore, the process is able to preserve memory about its previous values. It possesses a simple(More)
We consider a Markovian jumping process with two absorbing barriers, for which the waiting-time distribution involves a position-dependent coefficient. We solve the Fokker-Planck equation with boundary conditions and calculate the mean first passage time (MFPT) which appears always finite, also for the subdiffusive case. Then, for the case of the(More)
  • T Srokowski
  • Physical review. E, Statistical, nonlinear, and…
  • 2007
We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's(More)
  • T Srokowski
  • Physical review. E, Statistical, nonlinear, and…
  • 2001
The kangaroo process (KP) is characterized by various forms of covariance and can serve as a useful model of random noises. We discuss properties of that process for the exponential, stretched exponential, and algebraic (power-law) covariances. Then we apply the KP as a model of noise in the generalized Langevin equation and simulate solutions by a Monte(More)
We consider a Markovian jumping process which is defined in terms of the jump-size distribution and the waiting-time distribution with a position-dependent frequency, in the diffusion limit. We assume the power-law form for the frequency. For small steps, we derive the Fokker-Planck equation and show the presence of the normal diffusion, subdiffusion, and(More)
Using differential display mRNA techniques, the authors found cDNA of the heat shock 70 protein known as GRP75 overexpressed in ovarian cancer cell lines. In the current study, the authors used immunohistochemistry to characterize the expression pattern of GRP75 in ovarian carcinomas and compared it with epithelial tumors originating from the female(More)
A jumping process, defined in terms of the jump size and waiting time distributions, is presented. The jumping rate depends on the process value. The process, which is Markovian and stationary, relaxes to an equilibrium and is characterized by a power-law autocorrelation function. Therefore, it can serve as a model of 1/f noise as well as of the stochastic(More)
The random walk process in a nonhomogeneous medium, characterized by a Lévy stable distribution of jump length, is discussed. The width depends on a position: either before the jump or after that. In the latter case, the density slope is affected by the variable width and the variance may be finite; then all kinds of the anomalous diffusion are predicted.(More)
A general solution to the Chapman-Kolmogorov equation for a jumping process called the "kangaroo process" is derived. A special case of algebraic dependences is discussed in detail. In particular, simple asymptotic formulas for probability distribution are presented. It is demonstrated that there are two different classes of limiting stationary(More)