One Kind of Multiple Dimensional Markovian BSDEs with Stochastic Linear Growth Generators

In this article, we deal with a multiple dimensional coupled Markovian BSDEs system with stochastic linear growth generators with respect to volatility processes. An existence result is provided by using approximation techniques.Comment: arXiv admin note: text overlap with arXiv:1412.121

Existence of Nash Equilibrium Points for Markovian Nonzero-sum Stochastic Differential Games with Unbounded Coefficients

This paper is related to nonzero-sum stochastic differential games in the Markovian framework. We show existence of a Nash equilibrium point for the game when the drift is no longer bounded and only satisfies a linear growth condition. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with continuous coefficient and stochastic linear growth

Jeux différentiels stochastiques de somme non nulle et équations différentielles stochastiques rétrogrades multidimensionnelles

This dissertation studies the multiple players nonzero-sum stochastic differential games (NZSDG) in the Markovian framework and their connections with multiple dimensional backward stochastic differential equations (BSDEs). There are three problems that we are focused on. Firstly, we consider a NZSDG where the drift coefficient is not bound but is of linear growth. Some particular cases of unbounded diffusion coefficient of the diffusion process are also considered. The existence of Nash equilibrium point is proved under the generalized Isaacs condition via the existence of the solution of the associated BSDE. The novelty is that the generator of the BSDE is multiple dimensional, continuous and of stochastic linear growth with respect to the volatility process. The second problem is of risk-sensitive type, i.e. the payoffs integrate utility exponential functions, and the drift of the diffusion is unbounded. The associated BSDE is of multi-dimension whose generator is quadratic on the volatility. Once again we show the existence of Nash equilibria via the solution of the BSDE. The last problem that we treat is a bang-bang game which leads to discontinuous Hamiltonians. We reformulate the verification theorem and we show the existence of a Nash point for the game which is of bang-bang type, i.e., it takes its values in the border of the domain according to the sign of the derivatives of the value function. The BSDE in this case is a coupled multi-dimensional system, whose generator is discontinuous on the volatility process.Cette thèse traite les jeux différentiels stochastiques de somme non nulle (JDSNN) dans le cadre de Markovien et de leurs liens avec les équations différentielles stochastiques rétrogrades (EDSR) multidimensionnelles. Nous étudions trois problèmes différents. Tout d'abord, nous considérons un JDSNN où le coefficient de dérive n'est pas borné, mais supposé uniquement à croissance linéaire. Ensuite certains cas particuliers de coefficients de diffusion non bornés sont aussi considérés. Nous montrons que le jeu admet un point d'équilibre de Nash via la preuve de l'existence de la solution de l'EDSR associée et lorsque la condition d'Isaacs généralisée est satisfaite. La nouveauté est que le générateur de l'EDSR, qui est multidimensionnelle, est de croissance linéaire stochastique par rapport au processus de volatilité. Le deuxième problème est aussi relatif au JDSNN mais les payoffs ont des fonctions d'utilité exponentielles. Les EDSRs associées à ce jeu sont de type multidimensionnelles et quadratiques en la volatilité. Nous montrons de nouveau l'existence d’un équilibre de Nash. Le dernier problème que nous traitons, est un jeu bang-bang qui conduit à des hamiltoniens discontinus. Dans ce cas, nous reformulons le théorème de vérification et nous montrons l’existence d’un équilibre de Nash qui est du type bang-bang, i.e., prenant ses valeurs sur le bord du domaine en fonction du signe de la dérivée de la fonction valeur ou du processus de volatilité. L'EDSR dans ce cas est un système multidimensionnel couplé, dont le générateur est discontinu par rapport au processus de volatilité

Combining Transfer of TTF-1 and Pax-8 Gene: a Potential Strategy to Promote Radioiodine Therapy of Thyroid Carcinoma

Cotransfer of TTF-1 and Pax-8 gene to tumor cells, resulting in the reexpression of iodide metabolism-associated proteins, such as sodium iodide symporter (NIS), thyroglobulin (Tg), thyroperoxidase (TPO), offers the possibility of radioiodine therapy to non-iodide-concentrating tumor because the expression of iodide metabolism-associated proteins in thyroid are mediated by the thyroid transcription factors TTF-1 and Pax-8. The human TTF-1 and Pax-8 gene were transducted into the human thyroid carcinoma (K1 and F133) cells by the recombinant adenovirus, AdTTF-1 and AdPax-8. Reexpression of NIS mRNA and protein, but not TPO and Tg mRNA and protein, was detected in AdTTF-1-infected F133 cells, following with increasing radioiodine uptake (6.1~7.4 times), scarcely iodide organification and rapid iodide efflux (t1/2≈8 min in vitro, t1/2≈4.7 h in vivo).
In contrast, all of the reexpression of NIS, TPO and Tg mRNA and proteins in F133 cells were induced by the synergetic effect of TTF-1 and Pax-8. AdTTF-1 and AdPax-8 coinfected K1 and F133 cells could effectively accumulate radioiodine (6.6-7.5 times) and obviously retarded radioiodine retention (t1/2≈25-30 min in vitro, t1/2≈12 h in vivo) (p<0.05).
Accordingly, the effect of radioiodine therapy of TTF-1 and Pax-8 cotransducted K1 and
F133 cells (21-25% survival rate in vitro) was better than that of TTF-1-transducted cells
(40% survival rate in vitro) (p<0.05). These results indicate that single TTF-1 gene transfer may have limited efficacy of radioiodine therapy because of rapid radioiodine efflux. The cotransduction of TTF-1 and Pax-8 gene, with resulting NIS-mediated radioiodine accumulation and TPO and Tg-mediated radioiodine organification and intracellular retention, may lead to effective radioiodine therapy of thyroid carcinoma

Detector-decoy high-dimensional quantum key distribution

The decoy-state high-dimensional quantum key distribution provides a practical secure way to share more private information with high photon-information efficiency. In this paper, based on detector-decoy method, we propose a detector-decoy high-dimensional quantum key distribution protocol. Employing threshold detectors and a variable attenuator, we can estimate single-photon fraction of postselected events and Eves Holevo information under the Gaussian collective attack with much simpler operations in practical implementation. By numerical evaluation, we show that without varying source intensity and optimizing decoy-state intensity, our protocol could perform much better than one-decoy-state protocol and as well as the two-decoy-state protocol. Specially, when the detector efficiency is lower, the advantage of the detector-decoy method becomes more prominent

On the bang-bang type Nash equilibrium point for Markovian nonzero-sum stochastic differential game

In this paper, we study a nonzero-sum stochastic differential game in Markovian framework. We show the existence of the Nash equilibrium point which is discontinuous and of bang-bang type under natural conditions. The main tool is the notion of backward stochastic differential equations which, in our case, are multidimensional with discontinuous generators with respect to z component