We consider the problem of policy evaluation in a special class of Markov Decision Processes (MDPs) where the underlying Markov chains are large and sparse. We start from a stationary model equation that the limit of Temporal Difference (TD) learning satisfies, and develop a Robbins-Monro method consistently estimating its coefficients. Then we introduce the minimal residual approaches, which s...

In this work, we prove a comparison result for general class of nonlinear dispersive unidirectional wave equations. The nature one-dimensional waves occurs because convolution integral in space. For two specific choices the kernel function, Benjamin–Bona–Mahony equation and Rosenau that are particularly suitable to model water elastic waves, respectively, members class. We first an energy estim...

We investigate a class of Young diagrams growing via the addition unit cells and satisfying constraint that height difference between adjacent columns $\geq r$. In long time limit, appropriately re-scaled approach limit shape we compute for each integer $r\geq 0$. also determine shapes `diffusively' same evolving through removal proceed with equal rates.

in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

This paper studies the representation and large-sample consistency for nonparametric maximum likelihood estimators (NPMLEs) of an unknown baseline continuous cumulative-hazard-type function and parameter of group survival difference, based on right-censored two-sample survival data with marginal survival function assumed to follow a transformation model, a slight generalization of the class of ...