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We consider a homogenous fragmentation process with killing at an exponential barrier. With the help of two families of martingales we analyse the growth of the largest fragment for parameter values that allow for survival. In this respect…
We investigate the supports of extremal martingale measures with pre-specified marginals in a two-period setting. First, we establish in full generality the equivalence between the extremality of a given measure $Q$ and the denseness in…
For equality-constrained linear mixed-integer programs (MIP) defined by rational data, it is known that the subadditive dual is a strong dual and that there exists an optimal solution of a particular form, termed generator subadditive…
We consider a manufacturer who manages the end-of-life phase and takes one of the three actions at each period: (1) place an order, (2) use existing inventory, (3) stop holding inventory and use an outside/alternative source. Two examples…
We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…
A characterization of mixed Poisson processes in terms of disintegrations is proven. As a consequence some further characterizations of such processes via claim interarrival processes, martingales and claim measures are obtained. Some…
We consider immigration processes with binomial catastrophes and random survival parameters. Two sources of randomness are analyzed. In the first model, the survival parameter is independently resampled at each catastrophe. In the second…
Typical multi-task learning (MTL) methods rely on architectural adjustments and a large trainable parameter set to jointly optimize over several tasks. However, when the number of tasks increases so do the complexity of the architectural…
Many clinical studies evaluate the benefit of a treatment based on both survival and other continuous/ordinal clinical outcomes, such as Quality of Life scores. In these studies, when subjects die before the follow-up assessment, the…
It is well-known that the two-parameter Mittag-Leffler (ML) function plays a key role in Fractional Calculus. In this paper, we address the problem of computing this function, when its argument is a square matrix. Effective methods for…
We study non-parametric estimation of the value function of an infinite-horizon $\gamma$-discounted Markov reward process (MRP) using observations from a single trajectory. We provide non-asymptotic guarantees for a general family of…
Positively (resp. negatively) associated point processes are a class of point processes that induce attraction (resp. inhibition) between the points. As an important example, determinantal point processes (DPPs) are negatively associated.…
We develop a regression based primal-dual martingale approach for solving finite time horizon MDPs with general state and action space. As a result, our method allows for the construction of tight upper and lower biased approximations of…
In Markov Decision Processes (MDPs) with intermittent state information, decision-making becomes challenging due to periods of missing observations. Linear programming (LP) methods can play a crucial role in solving MDPs, in particular,…
In order to describe the extremal behaviour of some stochastic process $X$, approaches from univariate extreme value theory are typically generalized to the spatial domain. In particular, generalized peaks-over-threshold approaches allow…
This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
Over the past few decades, machine learning has been widely used to learn complex tasks. Reinforcement Learning (RL), inspired by human behavior, is a great example, as it involves developing specific behaviours for specific tasks. To…
Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive…
We consider nondeterministic probabilistic programs with the most basic liveness property of termination. We present efficient methods for termination analysis of nondeterministic probabilistic programs with polynomial guards and…