The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform

David Nualart - One of the best experts on this subject based on the ideXlab platform.

Paweł Sztonyk - One of the best experts on this subject based on the ideXlab platform.

  • Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise
    Potential Analysis, 2020
    Co-Authors: Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk
    Abstract:

    We consider the stochastic differential equation d X _ t = A ( X _ t −) d Z _ t , X _0 = x , driven by cylindrical α -stable process Z _ t in , where α ∈ (0,1) and d ≥ 2. We assume that the determinant of A ( x ) = ( a _ i j ( x )) is bounded away from zero, and a _ i j ( x ) are bounded and Lipschitz continuous. We show that for any fixed γ ∈ (0, α ) the semigroup P _ t of the process X _ t satisfies | P t f ( x ) − P t f ( y ) | ≤ c t − γ / α | x − y | γ | | f | | ∞ $|P_{t} f(x) - P_{t} f(y)| \le c t^{-\gamma /\alpha } |x - y|^{\gamma } ||f||_{\infty }$ for arbitrary bounded Borel Function f . Our approach is based on Levi’s method.

Hisashi Kikuchi - One of the best experts on this subject based on the ideXlab platform.

  • valley approximation for the Borel Function
    Physical Review D, 1992
    Co-Authors: Hisashi Kikuchi
    Abstract:

    A simple one-dimensional integral is investigated as a model for large-order estimation of the perturbative expansion in quantum mechanics with degenerate vacua. A Borel Function analysis allows us to separate nonperturbative contributions from perturbative ones. Issues such as the cancellation between the perturbative and nonperturbative contributions of ambiguity due to non-Borel summability and the large-order estimation in terms of a dispersion integral are discussed. A stationary-point approximation for the Borel Function is proposed to connect the simple integral to the quantum-mechanical case based on the new valley trajectory, which was recently formulated.

Youssef Ouknine - One of the best experts on this subject based on the ideXlab platform.

Tadeusz Kulczycki - One of the best experts on this subject based on the ideXlab platform.

  • Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise
    Potential Analysis, 2020
    Co-Authors: Tadeusz Kulczycki, Michał Ryznar, Paweł Sztonyk
    Abstract:

    We consider the stochastic differential equation d X _ t = A ( X _ t −) d Z _ t , X _0 = x , driven by cylindrical α -stable process Z _ t in , where α ∈ (0,1) and d ≥ 2. We assume that the determinant of A ( x ) = ( a _ i j ( x )) is bounded away from zero, and a _ i j ( x ) are bounded and Lipschitz continuous. We show that for any fixed γ ∈ (0, α ) the semigroup P _ t of the process X _ t satisfies | P t f ( x ) − P t f ( y ) | ≤ c t − γ / α | x − y | γ | | f | | ∞ $|P_{t} f(x) - P_{t} f(y)| \le c t^{-\gamma /\alpha } |x - y|^{\gamma } ||f||_{\infty }$ for arbitrary bounded Borel Function f . Our approach is based on Levi’s method.