Weak solutions to fuzzy stochastic differential equations under sub-fractional Brownian motion

In this paper, the fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (sfBm) are considered which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The sfBm is known as an extension of the Bm that preserves numerous attributes of fractional Brownian motion (fBm), but not the stationary of the increments. This property makes sfBm a possible candidate to models involving non-stationary increments, self-similarity, and long-range dependence which is suitable for the construction of stochastic models in finance and non-stationary queueing systems. We introduce an approximation approach to the fractional stochastic integrals, and a decomposition of the sfBm to find the existence and uniqueness of the weak solutions.

کلیدواژه ها:

Fuzzy sets ، Sub-fractional Brownian motion (sfBm) ، Fuzzy stochastic integral(FSI) ، Stochastic differential equation(SDE) ، Picard iteration method