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Fractional-order stochastic delayed neural networks with impulses: mean square finite-time contractive synchronization. [PDF]

Sci Rep
Palanisamy G, Kandasamy U, Rihan FA, Ben Said S.   +3 more
europepmc   +1 more source

Trajectory-based computational analysis of the quantum-classical transition in asymmetrically coupled spin-boson models. [PDF]

Comput Struct Biotechnol J
Uthailiang T, Issarakul P, Boonchui S.
europepmc   +1 more source

Path-integral evolution of multivariate systems with moderate noise [PDF]

L. Ingber
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Stochastic Integration Filter

IEEE Transactions on Automatic Control, 2013
The technical note deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the state, such as the extended Kalman filter, unscented Kalman filter, or the cubature Kalman filter, are based on computationally efficient but approximate integral evaluations.
Jindrich Duník, Ondrej Straka, Miroslav Simandl   +2 more
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On Stochastic Integration and Differentiation

Acta Applicandae Mathematica, 1999
This short note presents a method to identify the integrands \((\varphi_j)_{j=1}^n\) for a martingale \(\xi_t=\sum_{j=1}^n\int_0^t\varphi_j d\eta^j_t\), \((\eta^j)_{j=1}^n\) being independent Brownian motions, in a measurable way. The quintessence of the method is an \(L^2\)-limit of certain approximations to the quadratic covariation between \(\xi ...
Di Nunno, G., Rozanov, Yu. A.
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Stochastic integration with respect to a stochastic integral

Stochastic Analysis and Applications, 1997
In this paper we prove first the property of integration with respect to a measure defined by density,h(fm) = (hf)mor a measure mand functions f,h, taking values in Banach spaces. Then we use this result to prove the similar “associativity” property of the stochastic integralL.(K-X)= (LK) Xfor processes X,K,Ltaking values in Banach ...
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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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On a class of stochastic integrals

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1988
Let (\(\Omega\),\({\mathcal F},P)\) be a probability space. If a random variable X is from \(L^ r(dP)\), \(r>0\), then \(\| X\|_ r=(E| X|^ r)^{1/r}\). The notion of an \(S_{r,p}\) system \((r,p>0)\) was introduced by \textit{F. Moricz} [Acta Sci. Math. 38, 127-144 (1976; Zbl 0325.42007)] in the following way: A sequence \(\{X_ 1,X_ 2,...\}\) of random ...
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Stochastic Integrals and Differential Measures

Theory of Probability & Its Applications, 1988
The description of the class of measures with square integrable logarithmic derivative along a vector field and an operator field is obtained. This derivative coincides with an extended stochastic integral in the Gaussian case. The proofs are based on integration by parts.
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The Stochastic Integral

1990
In this chapter, we define (stochastic) Ito-integrals \(\int_0^t {HdM} \) H dM for local L 2 — martingales M and a fairly large class of adapted processes H. The integral is a random variable. It will be constructed as a suitable limit of Riemann-Stieltjes type approximations like $$\sum\limits_{i = 1}^n {{H_{{s_i}}} \cdot \left( {{M_{s{}_{i + 1}}}
Heinrich von Weizsäcker, Gerhard Winkler   +1 more
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