Proceedings of the International scientific and practical conference ―Science, technology and art in global context‖ (October 14-16, 2025) / Publisher website: www.naukainfo.com. – Warsaw, Poland, 2025. - 72 p.

65 a.s. Let be sufficiently large for , - For any we define the stopping time { , ) ( ) ( ) ( )} It is easy to see that is increasing as . Denote , whence a.s. If we prove that a.s., then a.s., and ( ) a.s. for all , ) . So we need to show that a.s. If it is not true, there are constants and ( ) , such that * + . Hence, there is such that * + ( ) By the Itô’s formula for the non-negative function ( ) ∑ ( ) , where positive constants we will define later, we obtain ( ( )) ,( ( ) ) * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + ( ) ( )( ( ) ) ( ) ∫ ( ) ( ) ( ) - ,( ( ) ) * ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) + ( ) ∫ ( ) ( ) ( ) - ∑ *( ( ) ) ( ) ( ) ∫ , ( ) ( ) ( ( ))- ̃ ( ) ∫ , ( ) ( ) ( ( ))- ̃ ( ) + ( ) For the function ( ) ( ) ( ( ) ( ) ( ) ∫ ( ) ( ) )

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