id	author	title	date	pages	extension	mime	words	sentence	flesch	summary	cache	txt
ejpam-3395	Njamen Njomen, Didier Alain; Djeutcha, Eric; Fono, Louis-Aime	Existence and Uniqueness Solution Under Non-Lipschiz Condition of the Mixed Fractional Heston's Model	2019	21	.pdf	application/pdf	7674	463	78	Using the successive ap- proximation method, the existence and uniqueness theorems of solutions to the following non-Lipschitz SDEs driven by mfBm are proved: X(t) = x0 + ∫ t 0 µ(s,X(s))ds+ ∫ t 0 σ1(s,X(s))dBs + ∫ t 0 σ2(s,X(s))dBHs , (3) where t ∈ [0, T ], x0 = ξ ∈ Rn is a random variable, 0 ≤ T < ∞, the process B represent a m-dimensional standard Ft-Brownian motion and the process BH represent a d-dimensional Ft-adapted fractional Brownian motion with the Hurst index H ∈ ( 3 4 , 1) defined in a same com- plete probability space (Ω,F ,P), and µ(t,X(t))[0, T ] × R → R,σ1(t,X(t)) : [Dϕ s u(s)]2dsdt < ∞ and for each sequence of partition (πn, n ∈ N) such that |πn| → 0 as n→ 0 n−1∑ i=0 E ∫ t (n) i+1 t (n) i ∫ t (n) j+1 t (n) j ∣∣∣Dϕ s u π(t (n) i )uπ(t (n) j )−Dϕ s u(t)Dϕ t u(s) ∣∣∣ dsdt and E[‖uπ − u‖2ϕ]2 tend to 0 as n→ 0, where πn = t (n) 0 < t (n) 1 < . . .	cache/ejpam-3395.pdf	txt/ejpam-3395.txt