We consider general singular control problems for random fields given by a stochastic partial differential equation (SPDE). We show that under some conditions the optimal singular control can be identified with the solution of a coupled system of SPDE and a reflected backward SPDE (RBSPDE). As an illustration we apply the result to a singular optimal harvesting problem from a population whose d...

I characterize backward induction in an epistemic model of perfect information games where players have common certain belief of the consistency of preferences rather than the rationality of choice. In this approach, backward induction corresponds to common certain belief of ‘belief in each subgame of opponent rationality’. At an interpretative level this result resembles the one established by...

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the associated BSDE does not admit any bounded solution. On the other hand, we prove that if the superquadratic BSDE admits a bounded solution, then there exist infin...

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with Lévy process. We obtain the existence and uniqueness of solutions to these equations by means of the penalization method. As its application, we give a probabilistic interpr...

We consider Backward Stochastic Diierential Equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coeecient which is Lipschitz-continuous in the state-and gains-processes, and convex in the gains-process. It is also shown that the minimal solution can be characterized as the unique so...

We consider backward stochastic differential equations with convex constraints on the gains (or intensity-of-noise) process. Existence and uniqueness of a minimal solution are established in the case of a drift coefficient which is Lipschitz continuous in the state and gains processes and convex in the gains process. It is also shown that the minimal solution can be characterized as the unique ...

Signal and image enhancement is considered in the context of a new type of diffusion process that simultaneously enhances, sharpens, and denoises images. The nonlinear diffusion coefficient is locally adjusted according to image features such as edges, textures, and moments. As such, it can switch the diffusion process from a forward to a backward (inverse) mode according to a given set of crit...

In this paper sensitivity analysis of a wideband backward-wave directional coupler due to fabrication imperfections is done using Monte Carlo method. For using this method, a random stochastic process with Gaussian distribution by 0 average and 0.1 standard deviation is added to the different geometrical parameters of the coupler and the frequency response of the coupler is estimated. The appli...

The introduction of a new product generation forces incumbents in network industries to rebuild their installed base to maintain an advantage over potential entrants. We study if backward compatibility can help moderate this process of rebuilding an installed base. Using a structural model of the US market for handheld game consoles, we show that backward compatibility lets incumbents transfer ...