A general form of the increments of two-parameter fractional wiener process

In the paper we study properties of solutions to stochastic differential inclusions and set-valued stochastic differential equations driven by a two-parameter Wiener process. We establish new connections between their solutions. We prove that attainable sets of solutions to such inclusions are subsets of values of multivalued solutions of associated set-valued stochastic equations. Next we show that every solution to stochastic inclusion is a continuous selection of a multivalued solution of an associated set-valued stochastic equation. Additionally we establish other properties of such solutions. The results obtained in the paper extends results dealing with this topic known both in deterministic and stochastic cases.

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Distribution Estimates for Functionals of the Two-Parameter Wiener Process

The Annals of Probability ◽

10.1214/aop/1176995940 ◽

1976 ◽

Vol 4 (6) ◽

pp. 977-982 ◽

Cited By ~ 17

Author(s):

Victor Goodman

Keyword(s):

Wiener Process ◽

Two Parameter

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Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region

Journal of Applied Probability ◽

10.1017/s0021900200048798 ◽

1975 ◽

Vol 12 (04) ◽

pp. 824-830

Author(s):

Arthur H. C. Chan

Keyword(s):

Lower Bound ◽

Gaussian Process ◽

Wiener Process ◽

Lower Bounds ◽

Upper Bound ◽

Exact Distribution ◽

Rectangular Region ◽

Process With Independent Increments ◽

Independent Increments ◽

Two Parameter

Let W (s, t), s, t ≧ 0, be the two-parameter Yeh–Wiener process defined on the first quadrant of the plane, that is, a Gaussian process with independent increments in both directions. In this paper, a lower bound for the distribution of the supremum of W (s, t) over a rectangular region [0, S]×[0, T], for S, T > 0, is given. An upper bound for the same was known earlier, while its exact distribution is still unknown.

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A general form of the increments of a two-parameter wiener process

Applied Mathematics-A Journal of Chinese Universities ◽

10.1007/bf02661991 ◽

1993 ◽

Vol 8 (1) ◽

pp. 54-63 ◽

Cited By ~ 2

Author(s):

Lin Zhengyan ◽

Lu Chuanrong

Keyword(s):

Wiener Process ◽

Two Parameter

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Some lower bounds for the distribution of the supremum of the Yeh-Wiener process over a rectangular region

Journal of Applied Probability ◽

10.2307/3212734 ◽

1975 ◽

Vol 12 (4) ◽

pp. 824-830 ◽

Cited By ~ 4

Author(s):

Arthur H. C. Chan

Keyword(s):

Lower Bound ◽

Gaussian Process ◽

Wiener Process ◽

Lower Bounds ◽

Upper Bound ◽

Exact Distribution ◽

Rectangular Region ◽

Process With Independent Increments ◽

Independent Increments ◽

Two Parameter

Let W (s, t), s, t ≧ 0, be the two-parameter Yeh–Wiener process defined on the first quadrant of the plane, that is, a Gaussian process with independent increments in both directions. In this paper, a lower bound for the distribution of the supremum of W (s, t) over a rectangular region [0, S]×[0, T], for S, T > 0, is given. An upper bound for the same was known earlier, while its exact distribution is still unknown.

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Distribution of the supremum of the two-parameter Yeh-Wiener process on the boundary

Journal of Applied Probability ◽

10.1017/s0021900200096078 ◽

1973 ◽

Vol 10 (04) ◽

pp. 875-880 ◽

Cited By ~ 1

Author(s):

S. R. Paranjape ◽

C. Park

Keyword(s):

Lower Bound ◽

Probability Distribution ◽

Wiener Process ◽

Two Parameter

Let D = [0, S] × [0, T] be a rectangle in E2 and X(s, t), (s, t)∈D, be a two parameter Yeh-Wiener process. This paper finds the probability distribution of the supremum of X(s, t) on the boundary of D by taking the limit of the probability distribution of the supremum of X(s, t) along certain paths as these paths approach the boundary of D. The probability distribution of the supremum of X(s, t) on the boundary of D gives a nice lower bound for the probability distribution of the supremum of X(s, t) on D, which is unknown.

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