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Generalized stochastic integrals and equations [PDF]
Transactions of the American Mathematical Society, 1970 1. Introduction. In his fundamental memoir [7] K. Ito introduced an important class of stochastic differential equations which are now known as Ito equations. These equations are based on his definitions of stochastic integrals with respect to Brownian motion and random measures with independent values.
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Path Integral Methods for Stochastic Differential Equations [PDF]
The Journal of Mathematical Neuroscience, 2015 revised ...
Chow, Carson C., Buice, Michael A.
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Generalized Fractional Calculus for Gompertz-Type Models
Mathematics, 2021 This paper focuses on the construction of deterministic and stochastic extensions of the Gompertz curve by means of generalized fractional derivatives induced by complete Bernstein functions.
Giacomo Ascione, Enrica Pirozzi
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SPDIEs and BSDEs Driven by Lévy Processes and Countable Brownian Motions
Journal of Function Spaces, 2016 The paper is devoted to solving a new class of backward stochastic differential equations driven by Lévy process and countable Brownian motions. We prove the existence and uniqueness of the solutions to the backward stochastic differential equations by ...
Pengju Duan
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Electronic Journal of Qualitative Theory of Differential Equations, 2012 In this paper, we consider a class of impulsive stochastic Volterra-Levin equations. By establishing a new integral inequality, some sufficient conditions for the existence and global attractivity of periodic solution for impulsive stochastic Volterra ...
dingshi li, Daoyi Xu
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Discrete Dynamics in Nature and Society, 2021 This paper presents a valid numerical method to solve nonlinear stochastic Itô–Volterra integral equations (SIVIEs) driven by fractional Brownian motion (FBM) with Hurst parameter H∈1/2,1.
Mengting Deng, Guo Jiang, Ting Ke
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Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In this paper, a force field is constructed along a given integral manifold in the presence of random perturbing forces. In this case, two types of integral manifolds are considered separately: 1) trajectories that depend on generalized coordinates and ...
M.I. Tleubergenov +2 more
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The 𝒮-Transform of Sub-fBm and an Application to a Class of Linear Subfractional BSDEs
Advances in Mathematical Physics, 2013 Let SH be a subfractional Brownian motion with index ...
Zhi Wang, Litan Yan
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On a Stochastic Integral Equation [PDF]
Proceedings of the Japan Academy, 1946 Not ...
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Quasisymplectic integrators for stochastic differential equations [PDF]
Physical Review E, 2004 7 pages, revtex, 6 eps ...
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