Ryan T. White

Bio: Ryan T. White is an academic researcher from Florida Institute of Technology. The author has contributed to research in topics: Computer science & Random walk. The author has an hindex of 5, co-authored 12 publications receiving 46 citations.

Discrete Operational Calculus in Delayed Stochastic Games

Abstract: This article deals with classes of antagonistic games with two players. A game is specified in terms of two `hostile' stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of the players is defeated. We target the first passage time $\tau_\rho$ of the defeat and the number of casualties to either player upon $\tau_\rho$. Here we validate our claim of analytic tractability of the general formulas obtained in [1] under various transforms.

Current Trends in Random Walks on Random Lattices

Abstract: In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.

On Reliability of Stochastic Networks

Abstract: In recent times we hear increasingly often about cyber attacks on various commercial and strategic sites that manage to escape any defense. In this article, we model such attacks on networks via stochastic processes and predict the time of a total or partial failure of a network including the magnitude of losses (such as the number of compromised nodes, lost weights, and a loss of other associated components relative to some fixed thresholds). To make such modeling more realistic we also assume that the information about the attacks is delayed as per random observations. We arrive at analytically and numerically tractable results demonstrated by examples and comparative simulation.

Discrete operational calculus in delayed stochastic games

Abstract: This article deals with classes of antagonistic games with two players. A game is specified in terms of two `hostile' stochastic processes representing mutual attacks upon random times exerting casualties of random magnitudes. The game ends when one of the players is defeated. We target the first passage time $\tau_\rho$ of the defeat and the number of casualties to either player upon $\tau_\rho$. Here we validate our claim of analytic tractability of the general formulas obtained in [1] under various transforms.

On Strategic Defense of Stochastic Networks

Abstract: This paper deals with the detection and prediction of losses due to cyber attacks waged on vital networks. The accumulation of losses to a network during a series of attacks is modeled by a 2-dimensional monotone random walk process as observed by an independent delayed renewal process. The first component of the process is associated with the number of nodes (such as routers or operational sites) incapacitated by successive attacks. Each node has a weight associated with its incapacitation (such as loss of operational capacity or financial cost associated with repair), and the second component models the cumulative weight associated with the nodes lost. Each component has a fixed threshold and crossing of a threshold by either component represents the network entering a critical condition. Results are given as joint functionals of the predicted time of the first observed threshold crossing along with the values of each component upon this time.

An Introduction To The Theory Of Point Processes

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Antagonistic One-To-N Stochastic Duel Game

Abstract: This paper is dealing with a multiple person game model under the antagonistic duel type setup The unique multiple person duel game with the one-shooting-to-kill-all condition is analytically solved and the explicit formulas are obtained to determine the time dependent duel game model by using the first exceed theory The model could be directly applied into real-world situations and an analogue of the theory in the paper is designed for solving the best shooting time for hitting all other players at once which optimizes the payoff function under random time conditions It also mathematically explains to build the marketing strategies for the entry timing for both blue and red ocean markets

A Versatile Stochastic Duel Game

Abstract: This paper deals with a standard stochastic game model with a continuum of states under the duel-type setup. It newly proposes a hybrid model of game theory and the fluctuation process, which could be applied for various practical decision making situations. The unique theoretical stochastic game model is targeted to analyze a two-person duel-type game in the time domain. The parameters for strategic decisions including the moments of crossings, prior crossings, and the optimal number of iterations to get the highest winning chance are obtained by the compact closed joint functional. This paper also demonstrates the usage of a new time based stochastic game model by analyzing a conventional duel game model in the distance domain and briefly explains how to build strategies for an atypical business case to show how this theoretical model works.

Current Trends in Random Walks on Random Lattices

Abstract: In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset of the real space. In this case we target the virtual first passage (or escape) time. Thus, unlike standard random walk problems, rather than crossing the boundary, we deal with the walker’s escape location arbitrarily distant from the boundary. In this paper, we give a short historical background on random walk, discuss various directions in the development of random walk theory, and survey most of our results obtained in the last 25–30 years, including the very recent ones dated 2020–21. Among different applications of such random walks, we discuss stock markets, stochastic networks, games, and queueing.