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Borel Function
The Experts below are selected from a list of 210 Experts worldwide ranked by ideXlab platform
David Nualart – 1st expert on this subject based on the ideXlab platform

Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
Stochastics and Dynamics, 2020CoAuthors: Mohamed Erraoui, Youssef Ouknine, David NualartAbstract:Let [Formula: see text] be a fractional Brownian sheet with Hurst parameters H, H′ ≤ 1/2. We prove the existence and uniqueness of a strong solution for a class of hyperbolic stochastic partial differential equations with additive fractional Brownian sheet of the form [Formula: see text], where b(ζ, x) is a Borel Function satisfying some growth and monotonicity assumptions. We also prove the convergence of Euler’s approximation scheme for this equation.

Hyperbolic Stochastic Partial Differential Equations with Additive Fractional Brownian Sheet
Stochastics and Dynamics, 2003CoAuthors: Mohamed Erraoui, Youssef Ouknine, David NualartAbstract:Let be a fractional Brownian sheet with Hurst parameters H, H′ ≤ 1/2. We prove the existence and uniqueness of a strong solution for a class of hyperbolic stochastic partial differential equations with additive fractional Brownian sheet of the form , where b(ζ, x) is a Borel Function satisfying some growth and monotonicity assumptions. We also prove the convergence of Euler’s approximation scheme for this equation.

Regularization of differential equations by fractional noise
Stochastic Processes and their Applications, 2002CoAuthors: David Nualart, Youssef OuknineAbstract:Let {BtH,t[set membership, variant][0,T]} be a fractional Brownian motion with Hurst parameter H. We prove the existence and uniqueness of a strong solution for a stochastic differential equation of the form , where b(s,x) is a bounded Borel Function with linear growth in x (case ) or a Holder continuous Function of order strictly larger than 11/2H in x and than in time (case ).
Paweł Sztonyk – 2nd expert on this subject based on the ideXlab platform

Strong Feller Property for SDEs Driven by Multiplicative Cylindrical Stable Noise
Potential Analysis, 2020CoAuthors: Tadeusz Kulczycki, Michał Ryznar, Paweł SztonykAbstract: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 – 3rd expert on this subject based on the ideXlab platform

valley approximation for the Borel Function
Physical Review D, 1992CoAuthors: Hisashi KikuchiAbstract:A simple onedimensional integral is investigated as a model for largeorder 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 nonBorel summability and the largeorder estimation in terms of a dispersion integral are discussed. A stationarypoint approximation for the Borel Function is proposed to connect the simple integral to the quantummechanical case based on the new valley trajectory, which was recently formulated.