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Exact simulation for solutions of one-dimensional Stochastic Differential Equations with discontinuous drift

Pierre Étoré, Miguel Martinez (2014)

ESAIM: Probability and Statistics

In this note we propose an exact simulation algorithm for the solution of (1) d X t = d W t + b ¯ ( X t ) d t , X 0 = x , d X t = d W t + b̅ ( X t ) d t,   X 0 = x, where b ¯ b̅is a smooth real function except at point 0 where b ¯ ( 0 + ) b ¯ ( 0 - ) b̅(0 + ) ≠ b̅(0 −) . The main idea is to sample an exact skeleton of Xusing an algorithm deduced from the convergence of the solutions of the skew perturbed equation (2) d X t β = d W t + b ¯ ( X t β ) d t + β d L t 0 ( X β ) , X 0 = x d X t β = d W t + b̅ ( X t β ) d t + β d L t 0 ( X β ) ,   X 0 = x towardsX solution of (1) as β ≠ 0 tends to 0. In this note, we show that this convergence...

Examples of bifurcation of periodic solutions to variational inequalities in κ

Milan Kučera (2000)

Czechoslovak Mathematical Journal

A bifurcation problem for variational inequalities U ( t ) K , ( U ˙ ( t ) - B λ U ( t ) - G ( λ , U ( t ) ) , Z - U ( t ) ) 0 for all Z K , a.a. t 0 is studied, where K is a closed convex cone in κ , κ 3 , B λ is a κ × κ matrix, G is a small perturbation, λ a real parameter. The main goal of the paper is to simplify the assumptions of the abstract results concerning the existence of a bifurcation of periodic solutions developed in the previous paper and to give examples in more than three dimensional case.

Existence and approximation results for gradient flows

Riccarda Rossi, Giuseppe Savaré (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

This note addresses the Cauchy problem for the gradient flow equation in a Hilbert space H u ...

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