scholarly journals Escape Rate and Conditional Escape Rate From a Probabilistic Point of View

2021 ◽  
Author(s):  
C. Davis ◽  
N. Haydn ◽  
F. Yang
Keyword(s):  
Point Of View ◽  
Escape Rate ◽  
Probabilistic Point

Nonlinear Time-Series Prediction with Missing and Noisy Data

1998 ◽  
Vol 10 (3) ◽  
pp. 731-747 ◽  
Author(s):  
Volker Tresp ◽  
Reimar Hofmann
Keyword(s):  
Time Series ◽  
Stochastic Simulation ◽  
Time Series Prediction ◽  
Noisy Data ◽  
Nonlinear Time Series ◽  
Point Of View ◽  
Data Set ◽  
Sunspot Data ◽  
Error Bars ◽  
Probabilistic Point

We derive solutions for the problem of missing and noisy data in nonlinear time-series prediction from a probabilistic point of view. We discuss different approximations to the solutions—in particular, approximations that require either stochastic simulation or the substitution of a single estimate for the missing data. We show experimentally that commonly used heuristics can lead to suboptimal solutions. We show how error bars for the predictions can be derived and how our results can be applied to K-step prediction. We verify our solutions using two chaotic time series and the sunspot data set. In particular, we show that for K-step prediction, stochastic simulation is superior to simply iterating the predictor.

scholarly journals Determination of Optimal Shipping Quantity for Perishable Goods under Probabilistic Supply

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Si-Yeong Lim ◽  
Sun Hur
Keyword(s):  
Probability Distribution Function ◽  
Point Of View ◽  
Perishable Products ◽  
Limited Time ◽  
Operational Costs ◽  
Perishable Goods ◽  
Mean And Variance ◽  
Probabilistic Point ◽  
Optimal Quantity

The problems of shipping and transporting perishable goods are commonly considered in the literature as significant topics, but rarely did researchers adopt a probabilistic point of view in their models. It is common in SCM environments that the participating entities’ behaviors are random and unpredictable and so can only be modeled in a probabilistic way. In this paper, we consider the shipping problem of determining the optimal quantity of perishable products with a limited time to be stored in the warehouse. The optimal quantity minimizes the overall operational costs including those of inventory and shipping. We develop a mathematical model, from which the probability distribution function, mean, and variance of the length of the build-up period are derived and we establish a cost function for determining the optimal shipping value.

scholarly journals On Railroad Tank Car Puncture Performance: Part II — Estimating Metrics

2016 ◽  
Author(s):  
David Y. Jeong ◽  
Michael E. Carolan ◽  
Benjamin Perlman
Keyword(s):  
Structural Damage ◽  
Performance Metrics ◽  
Hazardous Materials ◽  
Point Of View ◽  
Structural Performance ◽  
Regulatory Agencies ◽  
Puncture Resistance ◽  
Mathematical Relationships ◽  
Design Factors ◽  
Probabilistic Point

This paper is the second in a two-part series on the puncture performance of railroad tank cars carrying hazardous materials in the event of an accident. Various metrics are often mentioned in the open literature to characterize the structural performance of tank cars under accident loading conditions. One of the consequences in terms of structural damage to the tank during accidents is puncture. This two-part series of papers focuses on four metrics to quantify the performance of tank cars against the threat of puncture: (1) speed, (2) force, (3) energy, and (4) conditional probability of release. In Part I, generalized tank car impact scenarios were illustrated. Particular focus is given to the generalized shell impact scenario because performance-based requirements for shell puncture resistance are being considered by the regulatory agencies in United States and Canada. Definitions for the four performance metrics were given. Physical and mathematical relationships among these metrics were outlined. Strengths and limitations of these performance metrics were discussed. In this paper (Part II), the multi-disciplinary approach to develop engineering tools to estimate the performance metrics is described. The complementary connection between testing and modeling is emphasized. Puncture performance metrics, which were estimated from other sources, are compared for different tank car designs. These comparisons are presented to interpret the metrics from a probabilistic point of view. In addition, sensitivity of the metrics to the operational and design factors is examined qualitatively.

scholarly journals On the Option Pricing by the Binomial Model

2021 ◽  
Author(s):  
Nikos Halidias
Keyword(s):  
Sufficient Conditions ◽  
Fair Value ◽  
Point Of View ◽  
Binomial Model ◽  
No Arbitrage ◽  
Mathematical Arguments ◽  
Definition Of ◽  
Necessary And Sufficient ◽  
Probabilistic Point ◽  
Absence Of Arbitrage

In this note we study the binomial model applied to European, American and Bermudan type of derivatives. Our aim is to give the necessary and sufficient conditions under which we can define a fair value via replicating portfolios for any derivative using simple mathematical arguments and without using no arbitrage techniques. Giving suitable definitions we are able to define rigorously the fair value of any derivative without using concepts from probability theory or stochastic analysis therefore is suitable for students or young researchers. It will be clear in our analysis that if $e^{r \delta} \notin [d,u]$ then we can not define a fair value by any means for any derivative while if $d \leq e^{r \delta} \leq u$ we can. Therefore the definition of the fair value of a derivative is not so closely related with the absence of arbitrage. In the usual probabilistic point of view we assume that $d < e^{r \delta} < u$ in order to define the fair value but it is not clear what we can (or we can not) do in the cases where $e^{r \delta} \leq d$ or $e^{r \delta} \geq u$.

Linear least squares prediction in non-stochastic time series

1969 ◽  
Vol 1 (01) ◽  
pp. 111-122
Author(s):  
P. D. Finch
Keyword(s):  
Time Series ◽  
Possible Worlds ◽  
Probabilistic Approach ◽  
Point Of View ◽  
Frequency Interpretation ◽  
Set Up ◽  
Stochastic Time Series ◽  
Stochastic Time ◽  
Probabilistic Point ◽  
Conceptual Difficulties

Many problems arising in the physical and social sciences relate to processes which happen sequentially. Such processes are usually investigated by means of the theory of stationary stochastic processes, but there have been some attempts to develop techniques which are not subject to the conceptual difficulties inherent in the probabilistic approach. These difficulties stem from the fact that in practice one is often restricted to a single record which, from the probabilistic point of view, is only one sample from an ensemble of possible records. In some instances such a viewpoint seems artificial, and for some time series it is questionable whether any objective reality corresponds to the idea of an ensemble of possible time series. For example, as noted in Feller (1967), a theory of probability based on a frequency interpretation cannot meaningfully attach a probability to a statement such as “the sun will rise tomorrow”, because to do so one would have to set up a conceptual universe of possible worlds.

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