UDC 519.24

The problem of a discrete Markov diffusion abandoning an interval

/ D.V. Koroliouk // Kibernetika i sistemnyi analiz. — 2016. — Vol. 52, N 4. — P. 83–89.

We analyze the probability that a discrete Markov diffusion abandons an interval and its approximation by the Ornstein–Uhlenbeck process with asymptotically small diffusion is used. The problem of abandoning an interval is solved on the basis of action functional defined by the evolution component of the Ornstein–Uhlenbeck process. The exponential generator of discrete Markov diffusion generates the action functional by solving the variational problem (Frechet–Legendre transformation). Figs: 0. Tabl.: 0. Refs: 8 titles.

Keywords:

stochastic difference equation, action functional, variational problem, exponential generator, Ornstein–Uhlenbeck process, potential of a dynamic system.


FULL TEXT

Author(s):

Королюк Дмитрий Владимирович, кандидат физ.-мат. наук, старший научный сотрудник Института телекоммуникаций и глобального нформационного пространства НАН Украины, Киев,
e-mail: dimitri.koroliouk@ukr.net