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In this paper, we study a stationary control problem when the state process is a one di- mensional diffusion whose drift admits a unique, asymptotically stable equilibrium point
We introduce the concept of a mild solution for the right Hudson-Parthasarathy quantum stochastic differential equation, prove existence and uniqueness results, and show the
Stochastic partial differential equations of divergence form with discontinuous and unbounded coefficients are consid- ered in C 1 domains.. Existence and uniqueness results are
Theorem 1.3 establishes the relationships among the dual Hardy inequality (1.7), the first Dirichlet eigenvalue λ 0 and the first eigenvalue λ 0,T of transient diffusion
We prove that a stochastic flow of reflected Brownian motions in a smooth multidimensional domain is differentiable with respect to its initial position.. The derivative is a linear
b) Under the above conditions existence for the forward equation implies existence for the martingale problem and uniqueness for the forward equation for every initial
Abstract Following the Arnold-Marsden-Ebin approach, we prove local (global in 2-D) existence and uniqueness of classical (H¨ older class) solutions of stochastic Euler equation
Keywords infinite particle system, superprocess, interacting diffusion, clustering, Palm distri- bution, grove indexed systems of diffusions, grove indexed systems of branching
