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.

63 jumps, corresponding to the centered Poisson measure, but also the ―large‖ jumps, corresponding to the non-centered Poisson measure. In this paper we deal with the non-autonomous stochastic predator-prey model driven by the system of stochastic differential equations ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ) ( ) ( ) ( ) ∫ ( ) ( ) ̃ ( ) ∫ ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ) ( ) ( ) ( ) ∫ ( ) ( ) ̃ ( ) ∫ ( ) ( ) ( ) where ( ) and ( ) are the prey and predator population densities at time t , respectively, ( ) are independent standard one-dimensional Wiener processes, ( ) are independent Poisson measures, which are independent on ( ) ̃ ( ) ( ) ( ) , , ( )- ( ) ( ) are a finite measures on the Borel sets . In the following we will use the notations ( ) ( ( ) ( )) , ( ) , | ( )| √ ( ) ( ) , * | + ( ) ( ) ∫ , ( ) ( ( )- ( ) ∫ ( ( ) ( ) . For the bounded, continuous functions ( ) , ) , let us denote ( ) , ( ) . We prove that system (1) has a unique, positive, global (no explosion in a finite time) solution for any positive initial value. Let ( ) be a probability space, ( ) , are mutually independent standard one-dimensional Wiener processes on ( ) , and