82 citations · 116 across the 13 of their papers we have counts for
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On the Solution of Stochastic Functional Differential Equations via Memory Gap
Flavia Sancier, Salah Mohammed
We present an alternative proof for the existence of solutions of stochastic functional differential equations satisfying a global Lipschitz condition. The proof is based on an app…
Flows for Singular Stochastic Differential Equations with Unbounded Drifts
Olivier Menoukeu Pamen, Salah E. A. Mohammed
In this paper, we are interested in the following singular stochastic differential equation (SDE) $${\rm d} X_t = b(t,X_t) {\rm d} t + {\rm d} B_{t},\ 0\leq t\leq T,\ X_0 = x \in \…
Sobolev differentiable stochastic flows for SDEs with singular coefficients: Applications to the transport equation
Salah-Eldin A. Mohammed, Torstein K. Nilssen, Frank N. Proske
In this paper, we establish the existence of a stochastic flow of Sobolev diffeomorphisms \[\mathbb{R}^d\ni x\quad\longmapsto\quadϕ_{s,t}(x)\in \mathbb{R}^d,\qquad s,t\in\mathbb{R}…
A Delayed Black and Scholes Formula II
Mercedes Arriojas, Yaozhong Hu, Salah-Eldin Mohammed +1
This article is a sequel to [A.H.M.P]. In [A.H.M.P], we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic del…
A Delayed Black and Scholes Formula I
Mercedes Arriojas, Yaozhong Hu, Salah-Eldin Mohammed +1
In this article we develop an explicit formula for pricing European options when the underlying stock price follows a non-linear stochastic differential delay equation (sdde). We b…
The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations II: Existence of stable and unstable manifolds
Salah-Eldin A. Mohammed, Tusheng Zhang, Huaizhong Zhao
This article is a sequel to [M.Z.Z.1] aimed at completing the characterization of the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and…