On the mathematical structure of chemical kinetic models
... reactions. In particular, it is concerned with the system behavior away from equilibrium. Although the reaction equations capture the key interactions between the competing species, on their own they are not enough to determine the full system dynamics. Solving the dynamics of a chemical system mean ...
... reactions. In particular, it is concerned with the system behavior away from equilibrium. Although the reaction equations capture the key interactions between the competing species, on their own they are not enough to determine the full system dynamics. Solving the dynamics of a chemical system mean ...
PROBABILITY AND CERTAINTY
... could in this fashion give an exact utility measure of my dispositional certainty in a proposition. It would amount to the precise threshold of loss at which I would cease to be indifferent between the two options. So at low stakes I am certain of both, but there is a range of stakes such that I wou ...
... could in this fashion give an exact utility measure of my dispositional certainty in a proposition. It would amount to the precise threshold of loss at which I would cease to be indifferent between the two options. So at low stakes I am certain of both, but there is a range of stakes such that I wou ...
BROWNIAN MOTION AND THE STRONG MARKOV PROPERTY
... Definition 1.7. Let (S, Σ, µ) be a measure space. When µ(Σ) equals 1, this map is termed a probability measure and the associated measure space is called a probability space. We are now able to use this machinery to re-introduce some familiar concepts within probability theory. First, let us introdu ...
... Definition 1.7. Let (S, Σ, µ) be a measure space. When µ(Σ) equals 1, this map is termed a probability measure and the associated measure space is called a probability space. We are now able to use this machinery to re-introduce some familiar concepts within probability theory. First, let us introdu ...
Approximations of upper and lower probabilities by measurable
... analysis model for the probability distribution of this variable: the set of probability distributions P(Γ). There is, however, another set of probabilities that shall also be interesting for our purposes. It is based on the notions of upper and lower probabilities induced by multi-valued mapping. ...
... analysis model for the probability distribution of this variable: the set of probability distributions P(Γ). There is, however, another set of probabilities that shall also be interesting for our purposes. It is based on the notions of upper and lower probabilities induced by multi-valued mapping. ...
Stochastic Processes
... process in probability theory a process involving the operation of chance for example in radioactive decay every atom is subject to a fixed probability, stochastic process encyclopedia of mathematics - where is an arbitrary dimensional vector therefore the study of one dimensional processes occupies ...
... process in probability theory a process involving the operation of chance for example in radioactive decay every atom is subject to a fixed probability, stochastic process encyclopedia of mathematics - where is an arbitrary dimensional vector therefore the study of one dimensional processes occupies ...
Chapter 5 Elements of Probability Theory
... Two random variables y and z are said to be (pairwise) independent if, and only if, for any Borel sets B1 and B2 , IP(y ∈ B1 and z ∈ B2 ) = IP(y ∈ B1 ) IP(z ∈ B2 ). This immediately leads to the standard definition of independence: y and z are independent if, and only if, their joint distribution is ...
... Two random variables y and z are said to be (pairwise) independent if, and only if, for any Borel sets B1 and B2 , IP(y ∈ B1 and z ∈ B2 ) = IP(y ∈ B1 ) IP(z ∈ B2 ). This immediately leads to the standard definition of independence: y and z are independent if, and only if, their joint distribution is ...
