We prove that the law of the minimum m: = min t∈[,1] ξ(t) of the solution ξ to a one-dimensional stochastic differential equation with good nonlinearity has continuous density with respect to the Lebesgue measure. As a byproduct of the procedure, we show that the sets x∈ C([0 , 1]) : inf x≥ r have finite perimeter with respect to the law ν of the solution ξ(·) in L 2 (0 , 2).

On the Law of the Minimum in a Class of Unidimensional SDEs / Da Prato, G.; Lunardi, A.; Tubaro, L.. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 87:1(2019), pp. 93-104. [10.1007/s00032-019-00295-2]

On the Law of the Minimum in a Class of Unidimensional SDEs

Da Prato G.;Lunardi A.;
2019-01-01

Abstract

We prove that the law of the minimum m: = min t∈[,1] ξ(t) of the solution ξ to a one-dimensional stochastic differential equation with good nonlinearity has continuous density with respect to the Lebesgue measure. As a byproduct of the procedure, we show that the sets x∈ C([0 , 1]) : inf x≥ r have finite perimeter with respect to the law ν of the solution ξ(·) in L 2 (0 , 2).
2019
On the Law of the Minimum in a Class of Unidimensional SDEs / Da Prato, G.; Lunardi, A.; Tubaro, L.. - In: MILAN JOURNAL OF MATHEMATICS. - ISSN 1424-9286. - 87:1(2019), pp. 93-104. [10.1007/s00032-019-00295-2]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/2870506
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