About an unsolved stability problem for a stochastic difference equation with continuous time

Some Unsolved Problems in Stability and Optimal Control Theory of Stochastic Systems

“…Remark 3. It is clear that by the condition (16) we have µ = sup t≥0 σ 2 (t) < 2a and by the condition (17) we have µ = 0 < 2a. It means that the condition (20), (19) follows from each of the conditions (16) and (17) but not vice versa.…”

“…Some results of the stability theory for stochastic difference equations with continuous time are presented in [12]. Here we present the stability problem formulated more than ten years ago [16], which has not yet been solved. This problem is close enough to the one known result, but, nevertheless, it seams that it cannot be solved by known methods.…”

Unsolved problem about stability of stochastic difference equations with continuous time and distributed delay

“…However, there is a problem of stability of stochastic difference equations with continuous time and distributed delay, simply and clearly formulated more than 13 years ago [19], the solution of which has not yet been found. This problem was included also in the group of other unsolved problems that require solutions [22,23]. Some generalization of this unsolved problem is offered here in the hope that it will help solve it.…”

Behavior of solution of stochastic difference equation with continuous time under additive fading noise

“…1. Introduction Stochastic difference equations with continuous time are very popular in research (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]). But a problem that is considered here has not yet been encountered in the literature for this type of equations.…”