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We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by…
We study exploration in stochastic multi-armed bandits when we have access to a divisible resource that can be allocated in varying amounts to arm pulls. We focus in particular on the allocation of distributed computing resources, where we…
The basic question in perturbation analysis of Markov chains is: how do small changes in the transition kernels of Markov chains translate to chains in their stationary distributions? Many papers on the subject have shown, roughly, that the…
We study a two armed-bandit algorithm with penalty. We show the convergence of the algorithm and establish the rate of convergence. For some choices of the parameters, we obtain a central limit theorem in which the limit distribution is…
Various software fault prediction models and techniques for building algorithms have been proposed. Many studies have compared and evaluated them to identify the most effective ones. However, in most cases, such models and techniques do not…
This study explores the use of Recurrent Neural Networks (RNN) for real-time cryptocurrency price prediction and optimized trading strategies. Given the high volatility of the cryptocurrency market, traditional forecasting models often fall…
We use a neural network to identify the optimal solution to a family of optimal investment problems, where the parameters determining an investor's risk and consumption preferences are given as inputs to the neural network in addition to…
Many cryptocurrency brokers nowadays offer a variety of derivative assets that allow traders to perform hedging or speculation. This paper proposes an effective algorithm based on neural networks to take advantage of these investment…
We briefly review statistical models for the probability distribution of money developed in the econophysics literature since the late 1990s. In these models, economic transactions are modeled as random transfers of money between the agents…
Consider a system evolving according to an absorbing discrete-time Markov chain with known transition matrix. The state of the system is observed at two points in time, separated by an unknown number of generations. We are interested in…
We have studied the statistical mechanics of money circulation in a closed economic system. An explicit statistical formulation of the circulation velocity of money is presented for the first time by introducing the concept of holding time…
The Markov chain Monte Carlo method is a versatile tool in statistical physics to evaluate multi-dimensional integrals numerically. For the method to work effectively, we must consider the following key issues: the choice of ensemble, the…
Quantum computers are not yet up to the task of providing computational advantages for practical stochastic diffusion models commonly used by financial analysts. In this paper we introduce a class of stochastic processes that are both…
We study in this paper a generalized coupon collector problem, which consists in determining the distribution and the moments of the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an…
This study presents a rigorous mathematical approach to the optimization of round and betting policies in Blackjack, using Markov Decision Processes (MDP) and Expected Utility Theory. The analysis considers a direct confrontation between a…
We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…
The study of {\em balls-into-bins processes} or {\em occupancy problems} has a long history. These processes can be used to translate realistic problems into mathematical ones in a natural way. In general, the goal of a balls-into-bins…
Verification of infinite-state Markov chains is still a challenge despite several fruitful numerical or statistical approaches. For decisive Markov chains, there is a simple numerical algorithm that frames the reachability probability as…
This article is a tutorial on Markov chain Monte Carlo simulations and their statistical analysis. The theoretical concepts are illustrated through many numerical assignments from the author's book on the subject. Computer code (in Fortran)…
We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle…