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Author: Wagner, Wolfgang × Subject: probabilistic representation ×

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Now showing 1 - 4 of 4
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    A class of probabilistic models for the Schrödinger equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2014) Wagner, Wolfgang
    A class of stochastic particle models for the spatially discretized time-dependent Schrödinger equation is constructed. Each particle is characterized by a complex-valued weight and a position. The particle weights change according to some deterministic rules between the jumps. The jumps are determined by the creation of offspring. The main result is that certain functionals of the particle systems satisfy the Schrödinger equation. The proofs are based on the theory of piecewise deterministic Markov processes.
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    A random walk model for the Schrödinger equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Wagner, Wolfgang
    A random walk model for the spatially discretized time-dependent Schrödinger equation is constructed. The model consists of a class of piecewise deterministic Markov processes. The states of the processes are characterized by a position and a complex-valued weight. Jumps occur both on the spatial grid and in the space of weights. Between the jumps, the weights change according to deterministic rules. The main result is that certain functionals of the processes satisfy the Schrödinger equation.
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    A random cloud model for the Schrödinger equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Wagner, Wolfgang
    The paper is concerned with the construction of a stochastic model for the spatially discretized time-dependent Schrödinger equation. The model is based on a particle system with a Markov jump evolution. The particles are characterized by a sign (plus or minus), a position (discrete grid) and a type (real or imaginary). The jumps are determined by the creation of offsprings. The main result is the construction of a family of complex-valued random variables such that their expected values coincide with the solution of the Schrödinger equation.
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    A random cloud model for the Wigner equation
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Wagner, Wolfgang
    A probabilistic model for the Wigner equation is studied. The model is based on a particle system with the time evolution of a piecewise deterministic Markov process. Each particle is characterized by a real-valued weight, a position and a wave-vector. The particle position changes continuously, according to the velocity determined by the wave-vector. New particles are created randomly and added to the system. The main result is that appropriate functionals of the process satisfy a weak form of the Wigner equation.