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Marcus Stochastic Differential Equations: Representation of Probability Density

Mathematics
Marcus stochastic delay differential equations are often used to model stochastic dynamical systems with memory in science and engineering. It is challenging to study the existence, uniqueness, and probability density of Marcus stochastic delay ...
Fang Yang, Chen Fang, Xu Sun
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A stochastic representation for the Poisson–Vlasov equation [PDF]

Communications in Nonlinear Science and Numerical Simulation, 2008
9 Pages, 1 figure, VLASOVIA ...
Mendes, R. Vilela, Cipriano, Fernanda
openaire   +3 more sources

On the Representation of the Goursat Boundary Problem Solution for the First Order Partial Derivatives Stochastic Hyperbolic Equations

Известия Иркутского государственного университета: Серия "Математика", 2023
We study the standard canonical form of a stochastic analog of a system of linear partial differential equations of first order hyperbolic type with Goursat boundary conditions.
K.B. Mansimov, R.O. Mastaliyev
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On Wick calculus and its relationship with stochastic integration on spaces of regular test functions in the Lévy white noise analysis

Karpatsʹkì Matematičnì Publìkacìï, 2022
We deal with spaces of regular test functions in the Lévy white noise analysis, which are constructed using Lytvynov's generalization of a chaotic representation property.
N.A. Kachanovsky
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The recurrent temporal restricted Boltzmann machine captures neural assembly dynamics in whole-brain activity

eLife
Animal behaviour alternates between stochastic exploration and goal-directed actions, which are generated by the underlying neural dynamics. Previously, we demonstrated that the compositional Restricted Boltzmann Machine (cRBM) can decompose whole-brain ...
Sebastian Quiroz Monnens, Casper Peters, Luuk Willem Hesselink, Kasper Smeets, Bernhard Englitz   +4 more
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Extremal behavior of stochastic volatility models [PDF]

, 2005
Empirical volatility changes in time and exhibits tails, which are heavier than normal. Moreover, empirical volatility has - sometimes quite substantial - upwards jumps and clusters on high levels.
Lindner, Alexander M., Alexander Lindner, Vicky Fasen, Lindner, A., Claudia Klüppelberg, Fasen, V., Fasen, Vicky, Klüppelberg, Claudia   +7 more
core   +1 more source

Rotational Representations of Stochastic Matrices

The Annals of Probability, 1983
Let u denote Lebesgue measure on the interval \(X=[0,1)\). A stochastic matrix \(P=(p_{ij})\) is said to have a rotational representation if there exists a nonnegative number t and a partition \(S=\{S_ i\}^ n_{i=1}\) of X into nonempty sets \(S_ i\), which are each finite unions of intervals, such that \(p_{ij}=u(S_ i\cap f^{-1}(S_ j))/u(S_ i),\) 1 ...
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Path-integral representation for a stochastic sandpile [PDF]

Journal of Physics A: Mathematical and General, 2002
22 pages, 6 ...
Dickman, Ronald, Vidigal, Ronaldo
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A Stochastic Representation Of The Dynamics Of Sung Melody. [PDF]

, 2007
[TODO] Add abstract here.
Yasunori Ohishi, Masataka Goto, Katunobu Itou, Kazuya Takeda   +3 more
openaire   +1 more source

A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus

Entropy
We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field ...
John E. Gough
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