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The equation of symmetric Markovian random evolution in a plane

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  • Kolesnik, Alexander D.
  • Turbin, Anatoly F.

Abstract

A model of symmetric random evolution in a plane with , directions controlled by a homogeneous Poisson process is studied. A governing high-order hyperbolic equation is obtained. Its parabolic approximation is also given.

Suggested Citation

  • Kolesnik, Alexander D. & Turbin, Anatoly F., 1998. "The equation of symmetric Markovian random evolution in a plane," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 67-87, June.
    • Handle: RePEc:eee:spapps:v:75:y:1998:i:1:p:67-87
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    References listed on IDEAS

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    1. Foong, S. K. & Kanno, S., 1994. "Properties of the telegrapher's random process with or without a trap," Stochastic Processes and their Applications, Elsevier, vol. 53(1), pages 147-173, September.
    2. Orsingher, Enzo, 1985. "Hyperbolic equations arising in random models," Stochastic Processes and their Applications, Elsevier, vol. 21(1), pages 93-106, December.
    3. Orsingher, Enzo, 1990. "Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws," Stochastic Processes and their Applications, Elsevier, vol. 34(1), pages 49-66, February.
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    Cited by:

    1. Alexander D. Kolesnik, 2001. "Weak Convergence of a Planar Random Evolution to the Wiener Process," Journal of Theoretical Probability, Springer, vol. 14(2), pages 485-494, April.
    2. Cinque, Fabrizio & Orsingher, Enzo, 2023. "Random motions in R3 with orthogonal directions," Stochastic Processes and their Applications, Elsevier, vol. 161(C), pages 173-200.
    3. Giona, Massimiliano & Venditti, Claudia & Adrover, Alessandra, 2020. "On the long-term simulation of stochastic differential equations for predicting effective dispersion coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 543(C).
    4. Cinque, Fabrizio, 2022. "A note on the conditional probabilities of the telegraph process," Statistics & Probability Letters, Elsevier, vol. 185(C).
    5. Antonella Iuliano & Gabriella Verasani, 2024. "A Cyclic Random Motion in $$\mathbb {R}^3$$ R 3 Driven by Geometric Counting Processes," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-23, June.

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