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).File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.