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Existence of viable solutions for a nonconvex stochastic differential inclusion

Benoit Truong-Van, Truong Xuan Duc Ha (1997)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

For the stochastic viability problem of the form dx(t) ∈ F(t,x(t))dt+g(t,x(t))dW(t), x(t) ∈ K(t), where K, F are set-valued maps which may have nonconvex values, g is a single-valued function, we establish the existence of solutions under the assumption that F and g possess Lipschitz property and satisfy some tangential conditions.

Existence, uniqueness and convergence of a particle approximation for the Adaptive Biasing Force process

Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We study a free energy computation procedure, introduced in [Darve and Pohorille, J. Chem. Phys.115 (2001) 9169–9183; Hénin and Chipot, J. Chem. Phys.121 (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre et al., Nonlinearity21 (2008) 1155–1181],...

Expansion and random walks in SL d ( / p n ) : I

Jean Bourgain, Alex Gamburd (2008)

Journal of the European Mathematical Society

We prove that the Cayley graphs of SL d ( / p n ) are expanders with respect to the projection of any fixed elements in SL d ( ) generating a Zariski dense subgroup.

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