Quadratic Variation of Functionals of Brownian Motion

Wang, Albert T.

doi:10.1214/aop/1176995717

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/(/) = Lim {/?(/ + a /) -R(t T)}/h -Lim {R(t + A /) -R(t2

Convergence Of Solutions To Stochastic Differential Equations1

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Cited by 11 publications

(4 citation statements)

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“…This result was later extended to a wider class of processes (see [5], [2], [4]). The limit in (0.1) is L2-convergent (as well as almost sure convergent).…”

Section: /(/) = Lim {/?(/ + a /) -R(t T)}/h -Lim {R(t + A /) -R(tmentioning

confidence: 77%

Quadratic integration of Gaussian processes

Lin¹

1981

Proc. Amer. Math. Soc.

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“…This result was later extended to a wider class of processes (see [5], [2], [4]). The limit in (0.1) is L2-convergent (as well as almost sure convergent).…”

Section: /(/) = Lim {/?(/ + a /) -R(t T)}/h -Lim {R(t + A /) -R(tmentioning

confidence: 77%

Quadratic integration of Gaussian processes

Lin¹

1981

Proc. Amer. Math. Soc.

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show abstract

“…This result was later extended to a wider class of processes (see [5], [2], [4]). The limit in (0.1) is L2-convergent (as well as almost sure convergent).…”

Section: /(/) = Lim {/?(/ + a /) -R(t T)}/h -Lim {R(t + A /) -R(tmentioning

confidence: 77%

Quadratic Integration of Gaussian Processes

Lin¹

1981

Proceedings of the American Mathematical Society

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“…If X is a Wiener process, i.e. X W , then it was observed by Wang (1977) and F(W ) is a Dirichlet process assuming only that K f 2 (x) dx , I for every compact subset of RX (26)…”

Section: Convergence Of Solutions To Stochastic Differential Equationsmentioning

confidence: 99%

On the Convergence of Dirichlet Processes

Coquet¹,

Słomiński²

1999

Bernoulli

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For a given weakly convergent sequence fX n g of Dirichlet processes we show weak convergence of the sequence of the corresponding quadratic variation processes as well as stochastic integrals driven by the X n values provided that the condition UTD (a counterpart to the condition UT for Dirichlet processes) holds true. Moreover, we show that under UTD the limit process of fX n g is a Dirichlet process, too.

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Quadratic Variation of Functionals of Brownian Motion

Cited by 11 publications

References 0 publications

Quadratic integration of Gaussian processes

Quadratic integration of Gaussian processes

Quadratic Integration of Gaussian Processes

On the Convergence of Dirichlet Processes

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