Penalization method for a nonlinear Neumann PDE via weak solutions of reflected SDEs
, 2013 In this paper we prove an approximation result for the viscosity solution of a system of semi-linear partial differential equations with continuous coefficients and nonlinear Neumann boundary condition. The approximation we use is based on a penalization
Bahlali, Khaled +2 more
core +3 more sources
Homogenization of nonlinear stochastic partial differential equations in a general ergodic environment [PDF]
, 2013 In this paper, we show that the concept of sigma-convergence associated to stochastic processes can tackle the homogenization of stochastic partial differential equations.
Bensoussan A. +10 more
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On nonlinear Feynman-Kac formulas for viscosity solutions of semilinear parabolic partial differential equations with gradient-dependent nonlinearities [PDF]
arXiv, 2023 The classical Feynman-Kac identity represents solutions of linear partial differential equations in terms of stochastic differential euqations. This representation has been generalized to nonlinear partial differential equations on the one hand via backward stochastic differential equations and on the other hand via stochastic fixed-point equations. In
arxiv
Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility
Journal of Applied Mathematics, 2014 Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity ...
Min-Ku Lee +2 more
doaj +1 more source
Advances in Difference Equations, 2018 In this paper, based on the white noise theory for d-parameter Lévy random fields given by (Holden et al. in Stochastic Partial Differential Equations: A modeling, white noise functional approach, 2010), we develop a white noise frame for anisotropic ...
Xuebin Lü, Wanyang Dai
doaj +1 more source
Ergodicity for Stochastic Neutral Retarded Partial Differential Equations Driven by $α$-regular Volterra process [PDF]
arXiv, 2021 In this article, we study the ergodicity of neutral retarded stochastic functional differential equations driven by $\alpha$-regular Volterra process. Based on the equivalence between neutral retarded stochastic functional differential equations and the stochastic evolution equation, we get the ergodicity of neutral retarded stochastic functional ...
arxiv
Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions
, 2007 A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium.
A. Bensoussan +54 more
core +2 more sources
Unraveling the metastasis‐preventing effect of miR‐200c in vitro and in vivo
Molecular Oncology, Volume 19, Issue 4, Page 1029-1053, April 2025.Advanced tumors and ineffective cancer treatments can lead to metastases in distant organs. The sole expression of microRNA 200c (miR‐200c) in breast cancer cells is shown to significantly reduce metastasis formation in xenograft mouse models. Various in vitro analyses revealed impeded migratory behavior, upon miR‐200c expression, as one prerequisite ...
Bianca Köhler +12 more
wiley +1 more source
Известия высших учебных заведений. Поволжский регион: Физико-математические науки, 2021 Background. E. Nelson [1-3] introduced derivatives on the average in the works and over time, they began to be studied as a separate class of stochastic differential equations.
O.O. Zheltikova
doaj +1 more source
Hybrid deterministic stochastic systems with microscopic look-ahead dynamics [PDF]
, 2010 We study the impact of stochastic mechanisms on a coupled hybrid system consisting of a general advection-diffusion-reaction partial differential equation and a spatially distributed stochastic lattice noise model.
Katsoulakis, M. A. +2 more
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