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Two events A and B are called independent if their probabilities satisfy P(AB)=P(A)P(B) (Papoulis 1984, p. 40).

The characteristic escape rate from a stable state of a potential in the absence of signal.

An infinite-dimensional differential calculus on the Wiener space, also called stochastic calculus of variations.

A sequence X_1, X_2, ... of random variates is called Markov (or Markoff) if, for any n, F(X_n|X_(n-1),X_(n-2),...,X_1)=F(X_n|X_(n-1)), i.e., if the conditional distribution ...

An outcome is a subset of a probability space. Experimental outcomes are not uniquely determined from the description of an experiment, and must be agreed upon to avoid ...

Poisson's theorem gives the estimate (n!)/(k!(n-k)!)p^kq^(n-k)∼e^(-np)((np)^k)/(k!) for the probability of an event occurring k times in n trials with n>>1, p<<1, and np ...

A triple (S,S,P) on the domain S, where (S,S) is a measurable space, S are the measurable subsets of S, and P is a measure on S with P(S)=1.

The Rabinovich-Fabrikant equation is the set of coupled linear ordinary differential equations given by x^. = y(z-1+x^2)+gammax (1) y^. = x(3z+1-x^2)+gammay (2) z^. = ...

Given n mutually exclusive events A_1, ..., A_n whose probabilities sum to unity, then P(B)=P(B|A_1)P(A_1)+...+P(B|A_n)P(A_n), where B is an arbitrary event, and P(B|A_i) is ...

In statistics, a trial is a single performance of well-defined experiment (Papoulis 1984, p. 25), such as the flipping of a coin, the generation of a random number, the ...