PROSESSI TASODUFI

PROSESSI TASODUFI (pro s essi ehtimoli yo stokhasti), prosessi bo mururi zamon tagyir yoftani holati yagon siste­maro guyand, ki vobasta ba ittifoqe ba tarzhoi gunogun jarayon megirad va baroyash ehtimoli in yo on jarayon muqarrar shudaast. Harakati brouni, jarayoni turbulentii gazu moeot, jarayonpi elektri hangomi dar zanjir voqe budani fluktuatsiyahoi betartibi shiddat va quvvai jarayon (ba istiloh shavqunho), pahnoishi radiomavjho hangomi nogahon qat gardidani (ba istiloh fedingho) radiosignalho, ki dar natijai harakati havo yo yagon khalali digar ba vujud meoyad, misolhoi prosessi tasodufiand. Bisyor prosesshoi istehsoli, geofiziki, fiziologi va iqtisodi niz az jumlai prosesshoi tasodufiand.

Banoi dar tadqiqi Prosessi tasodufi istifo­da burdaii metodhoi matematiki boyad farz namud, ki holati lahzavii sistema ba tavri skhemavi chun nuqtai fazoi fazavi (fazoi kho­latho) — R ifoda yoftaast.

Nazariyai matematikii Prosessi tasodufi (hamchunin funksiyahoi beshtar umumi — funksiyahoi tasodufii argumenthoyashon dilkhoh) yake az sohai muhimi nazariyai ehtimoliyat meboshad. Prosessi tasodufi — prosessest, ki dar on t diskreti tagyir meyobadu sis­tema tanho vaziyathoi gunoguni okhirnokro sohib meshavad. Inro bo­ri avval matematiki rus A. A. Mar­kov (kaloni) tadqiq karda bud. Nazariyai Prosessi tasodufii ba vaqti befosila tagyiryobanda vobastaro matematikoni soveti B. B. Slutskiy, A. N. Kolmogorov va A. Ya. Khinchin, matematikoni amerikoi N. Viner, V. Feller va J. Duba, matematiki fransavi P. Levi va matematiki shved X. Kramer va digartadqiq va inkishof dodaand. Prosessi Mar­kov, prosesshoi tasodufii statsio­nari, hamchunin yak zumra zersinfho va mavridhoi umumiyatyoftai du sinfi zikrshuda (zanjiri Markov, prosesshoi shokha-shokha va gayra) az na­bili on sinfhoi Prosessi tasodufiaid, ki besh­tar tadqiq shudaand.

Ad.: Rozanov Yu. A.. Sluchaynie prosessi, M., 1971; Gikhman N. I.. Skorokhod A. V., Teoriya sluchaynikh prosessov, v 2-kh tomakh, M., 1971—73.

M. Muminov.