Markovian random evolution in Rn

Random Operators and Stochastic Equations

Volumn 9, Issue 2, 2001, Pages 139-160

  Samoilenko, I V ^a  

^a INSTITUTE OF MATHEMATICS   (Ukraine)

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[No Author keywords available]

Indexed keywords

EID: 0345099593     PISSN: 09266364     EISSN: 1569397X     Source Type: Journal    
DOI: 10.1515/rose.2001.9.2.139     Document Type: Article

References (28)

1. M. Barlett. Some problems associated with random velocity, Publ. Inst. Statist. Paris 6, 261-270(1957).
2. M. Barlett. A note on random walks at a constant speed, Adv. Appl. Probab. 10, 704-707 (1978).
3. V. Cane. Random walks and physical processes, Bull. Int. Statist Inst 42, 622-640 9 (1967).
4. V. Cane. Diffusion models with relativity effects, In: Gani, J. (Ed.), Perspectives in Probability and Statistics. Applied Probability Trust. Sheffield, 263-273 (1975).
5. W. Feller. An introduction to probability theory and its applications, v.l, John Wiley and Sons (1971).
6. V. A. Fok. In: Works of the State optical institute, 4, Leningrad opt. inst., 34 (1926). (in Russian).
7. S. Goldstein. On diffusion by discontinuous movements and the telegraph equations, Quart. J. Mech. Appl. Math. 4, 129-156 (1951).
8. L. Gorostiza. An invariance principle for a class of d-dimensional polygonal random functions, Trans. Amer. Math. Soc. 156, 413-445 (1973).
9. R. Griego, R. Hersh. Theory of random evolutions with applications to partial differential equations, Trans. Amer. Math. Soc. 156, 405-418 (1971).
10. R. Hersh. Random evolutions: a survey of results and problems, Rocky Mountain Math. Journal 4, 443-477(1974).
11. M. Kac. A stochastic model related to the telegrapher's equation, Rocky Mountain Math. Journal A, 497-510 (1974).
12. A. D. Kolesnik. On a model of Markovian random evolution in a plane, Ana-litical Methods of Investigation of Evolution of Stochastic Systems, Kiev, Inst. of Math., 55-61 (1989). (in Russian).
13. A. D. Kolesnik. The equations of Markovian random evolutions in a line, J. Appl Probab., 35 (1), to appear (1998).
14. A. D. Kolesnik, A. F. Turbin. Symmetric random evolutions in Dokl. Acad. Nauk Ukrain, 2, 10-11 (1990). (in Russian).
15. A. D. Kolesnik, A. F. Turbin. Infinitesimal hyperbolic operator of Markovian random evolutions, Dokl Acad. Nauk Ukrain, 1, 11-14 (1991). (in Russian).
16. N. S. Koshliakov and others. Partial derivatives equations of mathematical physics. Moskow, Higher School (1970). (in Russian).
17. E. Orsingher. Hyperbolic equations arising in random models, Stochastic Process. Appl, 21, 93-106 (1985).
18. E. Orsingher. A planar random motion governed by the two-dimensional telegraph equation, J. Appl. Probab., 23, 385-397 (1986). (Pubitemid 17483052)
19. E. Orsingher. Stochastic motions on the 3-sphere governed by wave and heat equations, J. Appl Probab., 24, 315-327 (1987).
20. E. Orsingher. Probability law, flow function, maximum distribution of wave-governed random motions and their connections with Kirchoff's laws, Stochastic Process. Appl, 34, 49-66 (1990).
21. E. Orsingher. Random motions governed by third-order equations, Adv. Appl. Probab., 22, 915-928 (1990).
22. E. Orsingher, B. Bassan. On a 2n-valued telegraph signal and related integrated process, Stochastics and Stochastics Rep., 38, 159-173 (1992).
23. E. Orsingher, A. D. Kolesnik. The explicit probability law of a planar random motion governed by a fourth order hyperbolic equation, Theor. Probab. Appl, 41, 451-459 (1996). (in Russian).
24. M. Pinsky. Differential equations with a small parameter and the central limit theorem for functions defined on a finite Markov chain, Zeit. Wahr., 9, 101-111 (1968).
25. M. Pinsky. Lectures on random evolutions. New York, World Scientific (1991).
26. n, International conference on mathematical modeling. Kiev, Inst, of Math., KSPU. (1998). (in Ukrainian).
27. E. V. Tolubinsky. Theory of transfer processes. Kiev, Naukova Dumka, (1969).
28. A. F. Turbin, D. Ja. Plotkin. Bessel equation and Bessel functions of high degree, Asymptotic methods in the problems of random evolution theory. Kiev, Inst, of Math. (1991). (in Russian).