The distribution density of square value probabilities functionality from trajectories of wiener process

Authors

  • Vitokhina NN Department of Theoretical and Mathematical Physics, Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia
  • Virchenko YP Department of Theoretical and Mathematical Physics, Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia
  • Zinchenko NA Department of Theoretical and Mathematical Physics, Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia
  • Mot’kina NN Department of Theoretical and Mathematical Physics, Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia
  • Esin VA Department of Theoretical and Mathematical Physics, Belgorod State University, 85, Pobedy St., Belgorod, 308015, Russia

Keywords:

stationary processes, casual Gaussian processes, Wiener process, the density of distribution of probabilities, additive functionality, return transformation of Laplace, calculating the successive approximations, accuracy assessment

Abstract

In the article authors develop an approach to calculating the statistic development probability for composite functions of square values in Gaussian casual process trajectories. Calculating distribution density for additive composite functions is based on standard Wiener process trajectories. Authors have developed a density formula for uniformly convergent decomposition, with x = 0. The convergence is exponentially fast. The calculation of the approximated probability is presented:

References

. Gikhman I.I., A.V. Skorokhod A.V., 1973. Theory of Random processes, V.II: Science. Publ. Nauka, Moscow. 641 pages.

. Ibragimov I.A., Rozanov Yu.A., 1970. Gaussian Random processes. Publ. Nauka Moscow: Science. 384 pages. (In Russian)

. Mazmanishvili A. S., 1987. Continual integration as a method of the solution of physical tasks. Kiev: Scientific thought. 224 pages. (In Russian)

. Arato M., 1982. Linear Stochastic Systems with Constant Coefficients. A Statistical Approach: Springer-Verlag. Berlin. 304 p.

. Ziegert A.J.F., 1957. A systematic approach to class problems in the theory of noise and other random phenomena. part II, examples. Trans. IRE. IT-3: 38-44.

. Zolotarev V.M., 1961. Concerning a Certain Probability Problem. Moscow: Theory Probability and its applications. 6, No. 2: 201-204. (In

Russian). Accessed from: http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=tvp&paperid=4769&option_lang=rus

. Vitokhina N.N., 2006. Distributions of probabilities in a problem of registration of stochastic radiation in quantum optics [Text]: Math PhD Thesis: 01.01.03 / N.N. Vitokhina. Belgorod. 155 pages. (In Russian)

. Virchenko Yu.P., Vitokhina N.N., 2003. About the local limit theorem for distribution of probabilities of additive square functionality from trajectories of complex-valued Wiener process. St. Petersburg: Mathematical models in education, science, and the industry. International Academy of Sciences of the higher school, St. Petersburg office. 48-50. (In Russian)

. Virchenko Yu.P., Vitokhina N. N, 2005. The distribution density of square values probabilities functionality from trajectories of the Wiener process. Belgorod: Scientific sheets of BELGU. Physical-Math sciences. No. 2(22). release 11. 16-22. (In Russian) available from: Virchenko Yu.P., Vitokhina N.N. The probability distribution density of random values of squared functional on Wiener process trajectories. ArXiv: mathph/0510028 vl.

. Kuo H.-H, 1979. Gaussian measures in Banachian spaces: World. Moscow. Publ. Springer-Verlag Berlin Heidelberg, Vol III, page.

pages. ISBN: 978-3-540-37508-1.

Downloads

Published

2024-02-26

How to Cite

Vitokhina, N. N., Virchenko, Y. P., Zinchenko, N. A., Mot’kina, N. N., & Esin, V. A. (2024). The distribution density of square value probabilities functionality from trajectories of wiener process. COMPUSOFT: An International Journal of Advanced Computer Technology, 8(06), 3192–3196. Retrieved from https://ijact.in/index.php/j/article/view/502

Issue

Section

Original Research Article

Similar Articles

<< < 9 10 11 12 13 14 15 16 17 18 > >> 

You may also start an advanced similarity search for this article.