Existence and uniqueness for solutions to fuzzy stochastic differential equations driven by local martingales under the non-Lipschitzian condition

Non-explosion of solutions to fuzzy stochastic differential equations with non-Lipschitz coefficients

“…(4) or Eq. (5) can be proven similar to the one in Fei [8]. The main tool of these studies is the generalized Bihari's inequality.…”

“…In fact, the properties of solutions to Eq. (3) under some conditions have been investigated in Fei [8], Malinowski [18,19] and Malinowski and Michta [20]. In this paper, we try to study the behaviour of the solutions to Eq.…”

Lebesgues-Stieltjes Integrals of Fuzzy Stochastic Processes with Respect to Finite Variation Processes

“…After the work [4], there are some references on set-valued integrals and fuzzy integrals. One may refer to papers such as [5]- [13] etc. and references therein.…”

Existence and Uniqueness of Solution for a Class of Stochastic Differential Equations

“…We also mention that, following Mao [14], many papers were devoted to improving the results of Mao [14] by weakening the Lipschitz conditions on coefficients (e.g., see Jiang and Wang [15], Fei [16], Caraballo et al [17], Wu et al [18], Jiang and Shen [19], Taniguchi [20], Fan and Jiang [21], Bao and Hou [22], Ren et al [23], Taniguchi [24], Wang and Huang [25], Lin [26], Xie [27], Fei [28], Ren and Zhang [29] and Zhang [30], etc.). In particular, Caraballo et al [17], Taniguchi [20], Bao and Hou [22], and Taniguchi [24] have studied the existence and uniqueness of solutions to SDEs under the non-Lipschitzian condition.…”