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$N$-SYMMETRY OF IT\^{o} STOCHASTIC DIFFERENTIAL EQUATION DRIVEN BY POISSON PROCESS
, 2016 Lie point symmetry transformation of the class of Itô stochastic differential equation driven by Poisson Processes was successfully carried out. We consider symmetries involving not only spatial and time variables (t, x), but also the Poisson process ...
A. M. Nass, E. Fredericks
semanticscholar +1 more source
Advances in Differential Equations, 2013 Choosing space Cg as the phase space, the existence, uniqueness and stability of the solution to neutral stochastic functional differential equations with infinite delay (short for INSFDEs) are studied in this paper.
Fengying Wei, Yuhua Cai
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Exploring Stochastic Fractional Delay Integrodifferential System
Asia Pacific Journal of Mathematics. This study examines the system of stochastic fractional delay integrodifferential equations with Gaussian noise. We employ the Picard-Lindelof successive approximation scheme for existence and uniqueness.
M. L. Maheswari, Karthik Muthusamy
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Functional integro‐differential stochastic evolution equations in Hilbert space
International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 141-161, 2003., 2003 We investigate a class of abstract functional integro‐differential stochastic evolution equations in a real separable Hilbert space. Global existence results concerning mild and periodic solutions are formulated under various growth and compactness conditions.
David N. Keck, Mark A. McKibben
wiley +1 more source
Dynamical behavior for a stochastic two-species competitive model
Open Mathematics, 2017 This paper deals with a stochastic two-species competitive model. Some very verifiable criteria on the global stability of the positive equilibrium of the deterministic system are established.
Xu Changjin, Liao Maoxin
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Periodicity in distribution. I. Discrete systems
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 2, Page 65-127, 2002., 2002 We consider the existence of periodic in distribution solutions to the difference equations in a Banach space. A random process is called periodic in distribution if all its finite‐dimensional distributions are periodic with respect to shift of time with one period. Only averaged characteristics of a periodic process are periodic functions.
A. Ya. Dorogovtsev
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Approximations of center manifolds for delay stochastic differential equations with additive noise
Advances in Nonlinear Analysis, 2023 This article deals with approximations of center manifolds for delay stochastic differential equations with additive noise. We first prove the existence and smoothness of random center manifolds for these approximation equations. Then we show that the Ck{
Wu Longyu +3 more
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Discretizing a backward stochastic differential equation
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 2, Page 103-116, 2002., 2002 We show a simple method to discretize Pardoux‐Peng′s nonlinear backward stochastic differential equation. This discretization scheme also gives a numerical method to solve a class of semi‐linear PDEs.
Yinnan Zhang, Weian Zheng
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Robust option replication for a Black-Scholes model extended with nondeterministic trends [PDF]
, 2012 Statistical analysis on various stocks reveals long range dependence behavior of the stock prices that is not consistent with the classical Black and Scholes model.
Kloeden, Peter E. +1 more
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A Haussmann‐Clark‐Ocone formula for functionals of diffusion processes with Lipschitz coefficients
International Journal of Stochastic Analysis, Volume 15, Issue 4, Page 357-370, 2002., 2002 We establish a martingale representation formula for functionals of diffusion processes with Lipschitz coefficients, as stochastic integrals with respect to the Brownian motion.
Khaled Bahlali +2 more
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