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Soft actor-critic energy management in three-phase unbalanced microgrids with lagrangian penalty constraints. [PDF]

Sci Rep
Cortés P, Tabares A, Bolaños R, Bonilla K.   +3 more
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On one-dimensional stochastic differential equations driven by stable processes

Lithuanian Mathematical Journal, 2000
It is considered the one-dimensional stochastic differential equation \[ X_t= x+ \int^t_0 b(s, X_{s-}) dZ_s,\qquad t\geq 0,\tag{\(*\)} \] where \(Z\) is a symmetry \(\alpha\)-stable Lévy process with \(\alpha\in (1,2]\) and \(b\) is a Borel function.
H Pragarauskas, Pragarauskas H
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On stochastic processes associated with relativistic stable distributions

Lithuanian Mathematical Journal, 2008
The author considers relativistic \(\alpha\)-stable Lévy processes and proves some distributional properties, like its exact Lévy triplet. Then he constructs the corresponding Ornstein-Uhlenbeck process. Finally he characterizes relativistic \(\alpha\)-stable mixed processes via its transition function an and the local characteristic triplet.
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An efficient algorithm for Levy stable stochastic processes

AIP Conference Proceedings, 1993
We present a new algorithm generating stochastic processes with a probability distribution very close to a Levy stable probability distribution characterized by the parameter α. The parameter α can be selected within the range 0.3≤α≤2. The algorithm is very efficient for 0.75≤α≤1.95.
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Fast, accurate algorithm for numerical simulation of Lévy stable stochastic processes

Physical Review E, 1994
We propose a fast and accurate algorithm generating L\'evy stable stochastic processes of arbitrary index \ensuremath{\alpha} ranging between 0.3 and 1.99. The scale parameter is also controllable. The algorithm is very fast when \ensuremath{\alpha} lies between 0.75 and 1.95.
Rosario N Mantegna
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Stable Manifolds for Stochastic Flows Induced by Lévy Processes on Lie Groups

Proceedings of the London Mathematical Society, 2001
Let \(G\) be a Lie group of non-compact type, \(K\) be a maximal compact subgroup, and \(A\) be a maximal abelian \(\text{Ad}(K)\)-invariant subgroup. Let \((\phi_t)\) be a right Lévy process on \(G\) having finite Lévy measure and satisfying some irreducibility and integrability condition. The Cartan decomposition is denoted by \(\phi_t g= k^g_t a^g_t
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Evolutionarily stable strategies for stochastic processes

Theoretical Population Biology, 2004
The classical definition of evolutionary stability assumes that the fitness of each phenotype is fully determined by the composition of phenotypes in the population and by the strategies of each of these phenotypes. In natural populations, however, stochasticity often plays a crucial role in determining the fitness of an individual and a deterministic ...
Dostálková, Iva, Kindlmann, Pavel
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Stationary min-stable stochastic processes

Probability Theory and Related Fields, 1984
We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneous Poisson process on the upper half-strip \([0,1]\times R_+\) and a group of \(L_ 1-isometries\).
de Haan, L. F. M., Pickands, James III
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Extremal stochastic integrals: a parallel between max-stable processes and α-stable processes

Extremes, 2005
The paper is devoted to construction of extremal stochastic integrals by random \(\alpha\)-Fréchet sup-measures and investigation of their properties, specially, connections with \(\alpha\)-stable integrals. A r.v. \(\xi\) has \(\alpha\)-Fréchet distribution \(F(\alpha,\sigma)\) if \(P\{\xi\leq x\}=\exp(-\sigma^\alpha x^{-\alpha})\), \(x>0\).
Stoev, Stilian A., Taqqu, Murad S.
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