Combinatorial basis and non-asymptotic form of the Tsallis entropy function
, 2008 Using a q-analog of Boltzmann's combinatorial basis of entropy, the non-asymptotic non-degenerate and degenerate combinatorial forms of the Tsallis entropy function are derived.
H. Suyari +3 more
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Models for time-varying moments using maximum entropy applied to a generalized measure of volatility [PDF]
We use an information-theoretic approach to interpret Engle's (1982) and Bollerslev's (1986) GARCH model as a model for the motion in time of the expected conditional second power moment.
Herrmann, Klaus
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A note on conditional arbitrage-free maximum entropy densities for simulative option pricing [PDF]
In this note we present a simple method to include the no-arbitrage condition into the derivation of conditional densities using the principle of maximum entropy.
Herrmann, Klaus
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Journal of Mathematical PhysicsFor the sandwiched Rényi entropy the conditional entropy can be defined two ways: H̃α↓(A|B)ρ,H̃α↑(A|B)ρ. In the limiting case, α = 1, both definitions consolidate into conditional entropy H(A|B) = S(AB) − S(B). The continuity inequality for conditional entropy H(A|B), called the Alicki–Fannes–Winter (AWF) inequality, shows that if the states are close ...
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Generalized Tsallis Entropy Reinforcement Learning and Its Application to Soft Mobile Robots
, 2020 In this paper, we present a new class of Markov decision processes (MDPs), called Tsallis MDPs, with Tsallis entropy maximization, which generalizes existing maximum entropy reinforcement learning (RL).
Sungjoon Choi +15 more
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Volatility models with innovations from new maximum entropy densities at work [PDF]
Generalized autoregressive conditional heteroskedasticity (GARCH) processes have become very popular as models for financial return data because they are able to capture volatility clustering as well as leptokurtic unconditional distributions which ...
Herrmann, Klaus +2 more
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Tsallis Entropy from Maximization of Entropy and the Condition of Stability
In a previous note (1), we argued that in the Maxwell-Boltzmann (Shannon) case, one may either maximize Shannon’s entropy: - Sum over i p(ei) ln(p(ei)) subject to the two a priori constraints: Sum over i p(ei)=1 and Sum over i ei p(ei) = Etotal or use reaction balance: e1+e2=e3+e4 and p(e1)p(e2)=p(e3)p(e4).
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A short characterization of relative entropy [PDF]
, 2019 We prove characterization theorems for relative entropy (also known as Kullback–Leibler divergence), q-logarithmic entropy (also known as Tsallis entropy), and q-logarithmic relative entropy. All three have been characterized axiomatically before, but we
Leinster, Thomas, Tom Leinster
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Tsallis Entropy from Maximization of Entropy and the Condition of Stability Part 2
In Part I, we argued that F(p(ei/T)) = -ei/T, where p(ei/T) is an unnormalized probability. We suggested that one may find Tsallis entropy from p(ei) power q dF/dp(ei) =1 ((1)), where F= lnq(p(ei)) and Tsallis entropy is: Sum over i p(ei) power q lnq(p(ei)). We argued that this was due to stability considerations.
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Tsallis Entropy from Maximization of Entropy and the Condition of Stability Part 3
In the note, we argue that statistical mechanics, at least with respect to Boltzmann/Shannon entropy and Tsallis entropy, may be formulated strictly through information related to -ei/T considerations. In fact, as argued in Part 2, there is no need for any notion of maximization of entropy subject to constraints or even reaction balance in the case of
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