RANDOM FIELDS: NON-ANTICIPATING DERIVATIVE AND DIFFERENTIATION FORMULAS

2007 ◽  
Vol 10 (03) ◽  
pp. 465-481 ◽  
Author(s):  
GIULIA DI NUNNO
Keyword(s):  
Random Fields ◽  
Random Variables ◽  
Space Time ◽  
Explicit Formulas ◽  
Stochastic Measure ◽  
Stochastic Derivative ◽  
Differentiation Formulas ◽  
General Stochastic

The non-anticipating stochastic derivative represents the integrand in the best L2-approximation for random variables by Itô non-anticipating integrals with respect to a general stochastic measure with independent values on a space–time product. In this paper some explicit formulas for this derivative are obtained.

Asymptotic analysis of the general stochastic epidemic with variable infectious periods

2001 ◽  
Vol 38 (01) ◽  
pp. 18-35 ◽  
Author(s):  
A. N. Startsev
Keyword(s):  
Asymptotic Analysis ◽  
Asymptotic Behaviour ◽  
Size Distribution ◽  
Random Variables ◽  
Independent Random Variables ◽  
Boundary Crossing ◽  
Total Size ◽  
Stochastic Epidemic ◽  
General Stochastic

A generalisation of the classical general stochastic epidemic within a closed, homogeneously mixing population is considered, in which the infectious periods of infectives follow i.i.d. random variables having an arbitrary but specified distribution. The asymptotic behaviour of the total size distribution for the epidemic as the initial numbers of susceptibles and infectives tend to infinity is investigated by generalising the construction of Sellke and reducing the problem to a boundary crossing problem for sums of independent random variables.

scholarly journals On the Density Functions of Integrals of Gaussian Random Fields

2013 ◽  
Vol 45 (02) ◽  
pp. 398-424 ◽  
Author(s):  
Jingchen Liu ◽  
Gongjun Xu
Keyword(s):  
Closed Form ◽  
Random Fields ◽  
Random Variables ◽  
Gaussian Random Fields ◽  
Density Functions ◽  
Exponential Functions ◽  
Asymptotic Bounds

In the paper we consider the density functions of random variables that can be written as integrals of exponential functions of Gaussian random fields. In particular, we provide closed-form asymptotic bounds for the density functions and, under smoothness conditions, we derive exact tail approximations of the density functions.

scholarly journals Space–Time Extremes in Short-Crested Storm Seas

2012 ◽  
Vol 42 (9) ◽  
pp. 1601-1615 ◽  
Author(s):  
Francesco Fedele
Keyword(s):  
Random Fields ◽  
Surface Displacement ◽  
Stochastic Approach ◽  
Space Time ◽  
Euler Characteristics ◽  
Sea State ◽  
Excursion Sets ◽  
Upper Limits ◽  
Wave Heights ◽  
Storm Model

Abstract This study develops a stochastic approach to model short-crested stormy seas as random fields both in space and time. Defining a space–time extreme as the largest surface displacement over a given sea surface area during a storm, associated statistical properties are derived by means of the theory of Euler characteristics of random excursion sets in combination with the Equivalent Power Storm model. As a result, an analytical solution for the return period of space–time extremes is given. Subsequently, the relative validity of the new model and its predictions are explored by analyzing wave data retrieved from NOAA buoy 42003, located in the eastern part of the Gulf of Mexico, offshore Naples, Florida. The results indicate that, as the storm area increases under short-crested wave conditions, space–time extremes noticeably exceed the significant wave height of the most probable sea state in which they likely occur and that they also do not violate Stokes–Miche-type upper limits on wave heights.

scholarly journals Space-time processing of random fields of signals in radar-tracking systems using adaptive stricture of unified algorithms and elements

2020 ◽  
pp. 41-45
Author(s):  
A. P. Shovkalyuk
Keyword(s):  
Random Fields ◽  
Optimization Problems ◽  
Negative Influence ◽  
Space Time ◽  
Spatial Structures ◽  
Time Processing ◽  
The Real ◽  
Time Optimization ◽  
First Time ◽  
Statistical Space

The efficiency of synthesized optimum algorithms of processing of random fields of signals is based on adequacy of mathematical model to the real phenomena which lay the foundation in mathematical models of useful and hindered signals. The basic and principal difference of the prospective approach to the development of new theoretical positions of the scientific – methodical means of space-time processing of random fields of signals from the known one is statistical space and time optimization with exception of mutual negative influence to each other. The advantage of the proposed approach is that synthesis becomes possible for the first time by solving statistical optimization problems at the spatial and temporal stages of processing. The use of kronecker-tensor product will make it possible to replace obsolete algorithms for processing multidimensional random received signals with better and more efficient ones, taking into account the real randomness of spatial structures and satisfying modern requirements of military science.

scholarly journals Statistics of the number of equilibria in random social dilemma evolutionary games with mutation

2021 ◽  
Vol 94 (8) ◽  
Author(s):  
Manh Hong Duong ◽  
The Anh Han
Keyword(s):  
Biological Diversity ◽  
Probability Distributions ◽  
Random Variables ◽  
Social Dilemma ◽  
Evolutionary Games ◽  
Explicit Formulas ◽  
Evolutionary Systems ◽  
Mutation Probability ◽  
Number Of Equilibria

Abstract In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game’s payoff entries are random variables. Using the replicator–mutator equations, we provide explicit formulas for the probability distributions of the number of equilibria as well as other statistical quantities. This analysis is highly relevant assuming that one might know the nature of a social dilemma game at hand (e.g., cooperation vs coordination vs anti-coordination), but measuring the exact values of its payoff entries is difficult. Our delicate analysis shows clearly the influence of the mutation probability on these probability distributions, providing insights into how varying this important factor impacts the overall behavioural or biological diversity of the underlying evolutionary systems. Graphic abstract

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