Existence of almost periodic solutions to some nonautonomous higher-order stochastic difference equations
Existence of almost periodic solutions to some nonautonomous higher-order stochastic difference equations
Abstract The paper studies the existence of almost periodic solutions to some nonautonomous higher-order stochastic difference equation of the form: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="block"> <m:mrow> <m:mi>X</m:mi> <m:mrow> <m:mo>(</m:mo> <m:mrow> <m:mi>t</m:mi> <m:mo>+</m:mo> <m:mi>n</m:mi> </m:mrow> <m:mo>)</m:mo> </m:mrow> <m:mo>+</m:mo> <m:munderover> <m:mo>∑</m:mo> <m:mrow> <m:mi>r</m:mi> <m:mo>=</m:mo> <m:mn>1</m:mn> </m:mrow> <m:mrow> <m:mi>n</m:mi> <m:mo>-</m:mo> <m:mn>1</m:mn> </m:mrow> </m:munderover> <m:mrow> <m:msub> …