49 citations · 90 across the 11 of their papers we have counts for
12 papers
Levy noise-induced self-induced stochastic resonance in a memristive neuron
Marius E. Yamakou, Tat Dat Tran
Self-induced stochastic resonance (SISR) is a subtle resonance mechanism requiring a nontrivial scaling limit between the stochastic and the deterministic timescales of an excitabl…
Differentiation of measures on complete Riemannian manifolds
Jürgen Jost, Hông Vân Lê, Tat Dat Tran
In this note we give a new proof of a version of the Besicovitch covering theorem, given in \cite{EG1992}, \cite{Bogachev2007} and extended in \cite{Federer1969}, for locally finit…
On the asymptotic behavior of the Diaconis and Freedman's chain in a multidimensional simplex
Marc Peigné, Tat Dat Tran
In this paper, we give out a setting of an Diaconis and Freedman's chain in a multidimensional simplex and consider its asymptotic behavior. By using techniques in random iterated…
Adaptive Bet-Hedging Revisited: Considerations of Risk and Time Horizon
Omri Tal, Tat Dat Tran
Models of adaptive bet-hedging commonly adopt insights from Kelly's famous work on optimal gambling strategies and the financial value of information. In particular, such models se…
Probabilistic morphisms and Bayesian nonparametrics
Jürgen Jost, Hông Vân Lê, Tat Dat Tran
In this paper we develop a functorial language of probabilistic morphisms and apply it to some basic problems in Bayesian nonparametrics. First we extend and unify the Kleisli cate…
Stochastic FitzHugh-Nagumo neuron model in excitable regime embeds a leaky integrate-and-fire model
Marius E. Yamakou, Tat Dat Tran, Luu Hoang Duc +1
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochas…
Ergodicity of scalar stochastic differential equations with Hölder continuous coefficients
Duc Hoang Luu, Tat Dat Tran, Jürgen Jost
It is well-known that for a one dimensional stochastic differential equation driven by Brownian noise, with coefficient functions satisfying the assumptions of the Yamada-Watanabe…
The uniqueness of hierarchically extended backward solutions of the Wright-Fisher model
Julian Hofrichter, Tat Dat Tran, Jürgen Jost
The diffusion approximation of the Wright-Fisher model of population genetics leads to partial differentiable equations, the so-called Kolmogorov equations, with an operator that d…
A hierarchical extension scheme for backward solutions of the Wright-Fisher model
Julian Hofrichter, Tat Dat Tran, Jürgen Jost
We develop an iterative global solution scheme for the backward Kolmogorov equation of the diffusion approximation of the Wright-Fisher model of population genetics. That model des…
A hierarchical extension scheme for solutions of the Wright-Fisher model
Julian Hofrichter, Tat Dat Tran, Jürgen Jost
We develop a global and hierarchical scheme for the forward Kolmogorov (Fokker-Planck) equation of the diffusion approximation of the Wright-Fisher model of population genetics. Th…
The evolution of moment generating functions for the Wright Fisher model of population genetics
Tat Dat Tran, Julian Hofrichter, Juergen Jost
We derive and apply a partial differential equation for the moment generating function of the Wright-Fisher model of population genetics.
A general solution of the Wright-Fisher model of random genetic drift
Tat-Dat Tran, Julian Hofrichter, Juergen Jost
We develop a general solution for the Fokker-Planck (Kolomogorov) equation representing the diffusion limit of the Wright-Fisher model of random genetic drift for an arbitrary numb…