A contemporary systematic review on deterministic numerical simulations of light propagation in head tissues. [PDF]
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Retardance and depolarization of brain white matter as markers for intraoperative delineation of brain tumors: experiments and simulations. [PDF]
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On solvability of stochastic differential inclusions with current velocities
Applicable Analysis, 2012An existence of solution theorem is obtained for stochastic differential inclusions given in terms of the so-called current velocities (direct analogues of ordinary velocity of deterministic systems) and quadratic mean derivatives (giving information on the diffusion coefficient) on the flat n-dimensional torus.
Yuri E Gliklikh
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Stochastic Invariance for Differential Inclusions
Set-Valued Analysis, 2000The first objective of this paper is to combine two ways for representing uncertainty through stochastic differential inclusions: a stochastic uncertainty driven by a Wiener process and a contingent uncertainty driven by a set-valued map. The second point consists to extend to stochastic differential inclusions the invariance theorem for nonstochastic ...
Aubin, Jean-Pierre +2 more
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Stochastic differential inclusions with Hilfer fractional derivative
Annals of the University of Craiova, Mathematics and Computer Science Series, 2022In this paper, we study the existence of mild solutions of Hilfer fractional stochastic differential inclusions driven by sub fractional Brownian motion in the cases when the multivalued map is convex and non convex. The results are obtained by using fixed point theorem. Finally an example is given to illustrate the obtained results.
Meryem Chaouche, Toufik Guendouzi
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Stochastic differential inclusions of Langevin type on Riemannian manifolds
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, 2001A set-valued analogue of the classical Langevin equation on a Riemannian manifold is introduced and several existence theorems of inclusions of Langevin type are proved. Let \(v:I\to T_{m_0}M\) be a continuous curve, \({ \mathcal S}v\) the unique \(C^1\)-curve \(\gamma: I\to M\) such that \(\gamma(0) =m_0\) and \(\dot\gamma (t)\) is parallel to the ...
Gliklikh, Yuri E., Obukhovskij, V.
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On the problem of stochastic differential inclusions
Journal of Soviet Mathematics, 1991zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Stochastic Approximations with Constant Step Size and Differential Inclusions
SIAM Journal on Control and Optimization, 2013We consider stochastic approximation processes with constant step size whose associated deterministic system is an upper semicontinuous differential inclusion. We prove that over any finite time span, the sample paths of the stochastic process are closely approximated by a solution of the differential inclusion with high probability.
Gregory Roth, William H. Sandholm
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Stochastic Differential Inclusions
2013A stochastic differential inclusion is formulated in terms of stochastic differentials of continuous semimartingales. In particular, concepts of strong and weak solutions of the inclusion \[ dx_t\in F(t,x_t)dt+G(t,x_t)dw_t \] are introduced. Here \(F,G:[0,1]\times R^n\to \text{Comp} (R^n)\) are Borel measurable set-valued mappings.
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Stabilization for Stochastic Nonlinear Differential Inclusion Systems with Time Delay
Circuits, Systems, and Signal Processing, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zongcai Jiang +2 more
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