Hitting times to spheres of Brownian motions with and without drifts

Hamana, Yuji; Matsumoto, Hiroyuki

doi:10.1090/proc/13136

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2016

2024

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Cited by 4 publications

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“…Moreover we use β x,y to denote x, y /|x| · |y| for x, y ∈ R d \ {0}. The explicit form of E x [e −λτv ] given in [11] immediately yields that L[L…”

Section: Laplace Transform Of Lmentioning

confidence: 99%

A formula for the expected volume of the Wiener sausage with constant drift

Hamana

Matsumoto

2016

Forum Mathematicum

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We consider the Wiener sausage for a Brownian motion with a constant drift up to time t associated with a closed ball. In the two or more dimensional cases, we obtain the explicit form of the expected volume of the Wiener sausage. The result says that it can be represented by the sum of the mean volumes of the multi-dimensional Wiener sausages without a drift. In addition, we show that the leading term of the expected volume of the Wiener sausage is written as κt(1+o [1]) for large t and an explicit form gives the constant κ. The expression is of a complicated form, but it converges to the known constant as the drift tends to 0.2010 Mathematics Subject Classification. Primary 60J65; Secondary 44A10.

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“…Moreover we use β x,y to denote x, y /|x| · |y| for x, y ∈ R d \ {0}. The explicit form of E x [e −λτv ] given in [11] immediately yields that L[L…”

Section: Laplace Transform Of Lmentioning

confidence: 99%