The exact probability distribution of a two-dimensional random walk

@article{Stadje1987TheEP,
  title={The exact probability distribution of a two-dimensional random walk},
  author={Wolfgang Stadje},
  journal={Journal of Statistical Physics},
  year={1987},
  volume={46},
  pages={207-216}
}
  • W. Stadje
  • Published 1987
  • Mathematics
  • Journal of Statistical Physics
A calculation is made of the exact probability distribution of the two-dimensional displacement of a particle at timet that starts at the origin, moves in straight-line paths at constant speed, and changes its direction after exponentially distributed time intervals, where the lengths of the straight-line paths and the turn angles are independent, the angles being uniformly distributed. This random walk is the simplest model for the locomotion of microorganisms on surfaces. Its weak convergence… 
Exact transient analysis of a planar random motion with three directions
Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of
Exact transient analysis of a planar random motion with three directions
Consider a planar random motion with constant velocity and three directions forming the angles ~ /6, 5 ~ /6 and 3 ~ /2 with the x -axis, such that the random times between consecutive changes of
A Pearson Random Walk with Steps of Uniform Orientation and Dirichlet Distributed Lengths
A constrained diffusive random walk of n steps in ℝd and a random flight in ℝd, which are equivalent, were investigated independently in recent papers (J. Stat. Phys. 127:813, 2007; J. Theor. Probab.
A four-dimensional random motion at finite speed
  • A. Kolesnik
  • Mathematics
    Journal of Applied Probability
  • 2006
We consider the random motion of a particle that moves with constant finite speed in the space ℝ 4 and, at Poisson-distributed times, changes its direction with uniform law on the unit four-sphere.
Stochastic velocity motions and processes with random time
TLDR
A class of random motions which models the motion of a particle on the real line with random velocity and subject to the action of the friction, and derives the probability distributions fixed the number of Poisson events.
On the Random Walk Microorganisms Cells Distribution on a Planar Surface and Its Properties
Abstract This paper presents an expansion of the Probability Density Function (PDF) at any time t for the distribution of the microorganism cells movement on the planar surface. A 2-dimensional
Exact probability distributions for noncorrelated random walk models
A stochastic model for the idealized locomotion of cells is studied. The cell is assumed to cover a polygonal line in ℝn, the times between turns are exponentially distributed and independent of the
A planar random motion with an infinite number of directions controlled by the damped wave equation
We consider the planar random motion of a particle that moves with constant finite speed c and, at Poisson-distributed times, changes its direction 0 with uniform law in [0, 27r). This model
Moving randomly amid scattered obstacles
We study a planar random motion at finite velocity performed by a particle which, at even-valued Poisson events, changes direction (each time chosen with uniform law in [0, 2π]). In other words this
Stochastic velocity motions and processes with random time
  • A. De Gregorio
  • Mathematics, Computer Science
    Advances in Applied Probability
  • 2010
TLDR
A class of random processes which models the motion of a particle on the real line with random velocity and subject to the action of friction, and derives the probability distributions for a fixed number of Poisson events.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
A generalized Pearson random walk allowing for bias
We calculate asymptotic values of the first two moments of a planar walk in which the step lengths depend on the direction of motion. The model is suggested by experiments on the locomotion of
A descriptive theory of cell migration on surfaces.
Linear statistical inference and its applications
Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation.
Convergence of Probability Measures
Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.
Table of Integrals, Series, and Products
Introduction. Elementary Functions. Indefinite Integrals of Elementary Functions. Definite Integrals of Elementary Functions. Indefinite Integrals of Special Functions. Definite Integrals of Special
Chemotaxis in Escherichia coli analysed by Three-dimensional Tracking
Chemotaxis toward amino-acids results from the suppression of directional changes which occur spontaneously in isotropic solutions.
...
1
2
...