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Dynamics of soliton propagation: bifurcation, chaos, and quantitative insights into the modified Camassa-Holm equation. [PDF]

Sci Rep
Alam MN, Ahmed SF, Ismael HF, Firdi MD, Badruddin IA, Javed S.   +5 more
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A Stochastic Integral Equation

SIAM Journal on Applied Mathematics, 1970
We investigate a stochastic integral equation of the form $x'(s) = y'(s) + \int_0^\alpha {K(s,t)dx(t)} $, where $y( s )$ is a process with orthogonal increments on the interval $T_\alpha = [0,\alpha ]$ and $K(s,t)$ is a continuous Fredholm or Volterra kernel on $T_\alpha \times T_\alpha $.
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Stochastic Integral Equations

1998
In this chapter we first present some random fixed point theorems for random operators. These results rely on classical continuation methods; in particular on the idea of an essential map. In section 11.3 our fixed point theory will then be applied to obtain a general existence principle for stochastic integral equations of Volterra type.
Donal O’Regan, Maria Meehan
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Numerical integration of stochastic differential equations

Journal of Statistical Physics, 1988
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Greiner, A., Strittmatter, W., Honerkamp, J.   +2 more
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Stochastic product integration and stochastic equations

1987
A standard method in deterministic product (or multiplicative) integration for integrating measures (or w.r.t measures) is to exploit Radon-Nikodym property. This technique does not extend to stochastic product integration w.r.t semimartingales. We introduce in this article a multiplicative operator functional (MOF) method to define stochastic product ...
L. Hazareesingh, D. Kannan
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Stochastic multisymplectic integrator for stochastic KdV equation

AIP Conference Proceedings, 2012
In this paper we investigate the stochastic multisymplectic methods to solve the stochastic partial differential equation. The stochastic KdV equations are considered. Besides conserving the multi-symplectic structure of original equation, the stochastic multi-symplectic methods are also investigated for the conservation of various conservation laws ...
Shanshan Jiang, Lijin Wang, Jialin Hong
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Stochastic Integrals and Stochastic Differential Equations

1985
Roughly speaking, stochastic differential equations are differential equations driven by Gaussian white noise. Here, we are using the term “stochastic differential equations” in a restricted sense and not merely to denote differential equations with some probabilistic aspects. The importance of.
Eugene Wong, Bruce Hajek
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Abstract stochastic integral equation involving a vector generalized Stochastic integral

Mathematical Notes of the Academy of Sciences of the USSR, 1991
See the review in Zbl 0729.60044.
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Numerical Integration of Stochastic Differential Equations

Bell System Technical Journal, 1979
In a previous paper, a method was presented to integrate numerically nonlinear stochastic differential equations (SDEs) with additive, Gaussian, white noise. The method, a generalization of the Range Kutta algorithm, extrapolates from one point to the next applying functional evaluations at stochastically determined points.
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