quadratic variation

English Term (puo:englishTerm)

quadratic variation

Definition of term (puo:definition)

Suppose that Xt is a real-valued stochastic process defined on a probability space
{\displaystyle (\Omega ,{\mathcal
{F}},\mathbb {P} )} and with time index t ranging over the non-negative real numbers. Its quadratic variation is the process, written as [X]t, defined as {\displaystyle [X]_{t}=\lim _{\Vert P\Vert \rightarrow 0}\sum
_{k=1}^{n}(X_{t_{k}}-X_{t_{k-1}})^{2}} where P ranges over partitions of the interval [0,t] and the norm of the partition P is the mesh. This limit, if it exists, is defined using convergence in probability. Note that a process may be of finite quadratic variation in the sense of the definition given here and its paths be nonetheless almost surely of infinite 2-variation for every t>0 in the classical sense of taking the supremum of the sum over all partitions / this is in particular the case for Brownian Motion.

Sesotho Term (puo:sesothoTerm)

khwadrethike varieishene

Afrikaans Term (puo:afrikaansTerm)

kwadratiese variasie

PanSALB Approved Languages (schema:status)

Sesotho

Afrikaans

Subject Field (schema:isPartOf)

Mathematics