Strong solution of Itô type set-valued stochastic differential equation

Stochastic integral with respect to set-valued square integrable martingales

“…In [22], Li and Li discussed more properties of the Lebesgue integral of set-valued stochastic processes. We also would like to refer to related works such as [5,23,24,32] and so on.…”

“…Hiai and Umegaki gave more general definition of conditional expectation of a set-valued random variable in [10] so that the theory of set-valued martingales could be developed deeply and extensively. There are many works in this area, for instance, [9][10][11][12][25][26][27][28][29][30][31][35][36][37]41,44,45]. But it is necessary to investigate set-valued square integrable martingales.…”

Set-Valued Stochastic Equation with Set-Valued Square Integrable Martingale

“…M. Malinowski et al discussed the setvalued stochastic integral driven by semi-martingale and the set-valued stochastic differential equations driven by semi-martingale in [7]. J. Li et al discussed setvalued stochastic Lebesgue integral and set-valued stochastic differential equaton in [8,9,10]. Puri and Ralescu defined fuzzy set-valued martingales and proved convergence theorems of fuzzy set-valued martingales in [11].…”

“…J. Li et al discussed the space of fuzzy set-valued square integrable martingales in [12] and fuzzy set-valued stochastic Lebesgue integral in [13]. In this paper, we shall give the set-valued stochastic integral equation : the first integral is set-valued stochastic Lebesgue integral (see [9,10]), the second integral is set-valued square integrable martingale integral (see [6]). Aumann integral measurable theorem of the second integral shall be given.…”

Properties of Solutions to Stochastic Set Differential Equations under Non-Lipschitzian Coefficients

“…In [27][28][29][30][31], the set-valued random differential equations are studied. The strong solution of Itô type set-valued stochastic differential equation is analyzed in [32].…”