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Doob (1996) defines a stochastic process as a family of random variables {x(t,-),t in J} from some probability space (S,S,P) into a state space (S^',S^'). Here, J is the ...

The study of random geometric structures. Stochastic geometry leads to modelling and analysis tools such as Monte carlo methods.

A stochastic approximation method that functions by placing conditions on iterative step sizes and whose convergence is guaranteed under mild conditions. However, the method ...

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

Differential calculus is that portion of "the" calculus dealing with derivatives. Among his many other talents, Major General Stanley in Gilbert and Sullivan's operetta the ...

Multivariable calculus is the branch of calculus that studies functions of more than one variable. Partial derivatives and multiple integrals are the generalizations of ...

An early name for calculus of variations. The term is also sometimes used in place of predicate calculus.

Integral calculus is that portion of "the" calculus dealing with integrals. Among his many other talents, Major General Stanley in Gilbert and Sullivan's operetta The Pirates ...

The study of an extension of derivatives and integrals to noninteger orders. Fractional calculus is based on the definition of the fractional integral as ...

The study, first developed by Boole, of shift-invariant operators which are polynomials in the differential operator D^~. Heaviside calculus can be used to solve any ordinary ...