References of "Journal of Theoretical Probability"
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See detailFunctional inequalities for Feynman-Kac semigroups
Thompson, James UL

in Journal of Theoretical Probability (2019)

Using stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main results is a derivative formula which ... [more ▼]

Using stochastic analysis, we prove various gradient estimates and Harnack inequalities for Feynman-Kac semigroups with possibly unbounded potentials. One of the main results is a derivative formula which can be used to characterize a lower bound on Ricci curvature using a potential. [less ▲]

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See detailHausdorff dimension of the range and the graph of stable-like processes
Yang, Xiaochuan UL

in Journal of Theoretical Probability (2018)

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See detailDerivatives of Feynman-Kac Semigroups
Thompson, James UL

in Journal of Theoretical Probability (2018)

We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of ... [more ▼]

We prove Bismut-type formulae for the first and second derivatives of a Feynman-Kac semigroup on a complete Riemannian manifold. We derive local estimates and give bounds on the logarithmic derivatives of the integral kernel. Stationary solutions are also considered. The arguments are based on local martingales, although the assumptions are purely geometric. [less ▲]

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See detailReflecting diffusion semigroup on manifolds carrying geometric flow
Cheng, Li Juan UL; Zhang, Kun

in Journal of Theoretical Probability (2017), 30(4), 1334-1368

Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differentiable manifold $M$ with boundary $\partial M$, where $\Delta_t$ is the Laplacian operator, induced by a time dependent metric $g_t ... [more ▼]

Let $L_t:=\Delta_t+Z_t$ for a $C^{1,1}$-vector field $Z$ on a differentiable manifold $M$ with boundary $\partial M$, where $\Delta_t$ is the Laplacian operator, induced by a time dependent metric $g_t$ differentiable in $t\in [0,T_c)$. We first establish the derivative formula for the associated reflecting diffusion semigroup generated by $L_t$; then construct the couplings for the reflecting $L_t$-diffusion processes by parallel displacement and reflection, which are applied to gradient estimates and Harnack inequalities of the associated heat semigroup; and finally, by using the derivative formula, we present a number of equivalent inequalities for a new curvature lower bound and the convexity of the boundary, including the gradient estimates, Harnack inequalities, transportation-cost inequalities and other functional inequalities for diffusion semigroups. [less ▲]

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See detailClassical and free fourth moment theorems: universality and thresholds
Nourdin, Ivan UL; Peccati, Giovanni UL; Poly, Guillaume et al

in Journal of Theoretical Probability (2016), 29(2), 653-680

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See detailMartingales on manifolds with time-dependent connection
Guo, Hongxin UL; Philipowski, Robert UL; Thalmaier, Anton UL

in Journal of Theoretical Probability (2015), 28(3), 1038-1062

We define martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Arnaudon, Coulibaly and ... [more ▼]

We define martingales on manifolds with time-dependent connection, extending in this way the theory of stochastic processes on manifolds with time-changing geometry initiated by Arnaudon, Coulibaly and Thalmaier (2008). We show that some, but not all properties of martingales on manifolds with a fixed connection extend to this more general setting. [less ▲]

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See detailDistributional transformations without orthogonality relations
Döbler, Christian UL

in Journal of Theoretical Probability (2015)

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See detailCentral and non-central limit theorems in a free probability setting
Nourdin, Ivan UL; Taqqu, Murad

in Journal of Theoretical Probability (2014), 27(1), 220-248

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See detailA quantitative central limit theorem for linear statistics of random matrix eigenvalues
Döbler, Christian UL; Stolz, Michael

in Journal of Theoretical Probability (2014)

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See detailRate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion
Azmoodeh, Ehsan UL; Viitasaari, Lauri

in Journal of Theoretical Probability (2013)

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a ... [more ▼]

In this article, an uniform discretization of stochastic integrals $\int_{0}^{1} f'_-(B_t)\ud B_t$, where $B_t$ denotes the fractional Brownian motion with Hurst parameter $H \in (\frac{1}{2},1)$, for a large class of convex functions $f$ is considered. In $\big[$\cite{a-m-v}, Statistics \& Decisions, \textbf{27}, 129-143$\big]$, for any convex function $f$, the almost sure convergence of uniform discretization to such stochastic integral is proved. Here we prove $L^r$- convergence of uniform discretization to stochastic integral. In addition, we obtain a rate of convergence. It turns out that the rate of convergence can be brought arbitrary close to $H - \frac{1}{2}$. [less ▲]

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See detailAsymptotic theory for fractional regression models via Malliavin calculus
Bourguin, Solesne UL; Tudor, C.A.

in Journal of Theoretical Probability (2012), 25(2), 536-564

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See detailCentral limit theorems for multiple Skorohod integrals
Nourdin, Ivan UL; Nualart, David

in Journal of Theoretical Probability (2010), 23(1), 39-64

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See detailExact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion
Neuenkirch, Andreas; Nourdin, Ivan UL

in Journal of Theoretical Probability (2008), 20(4), 871-899

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See detailStable convergence of multiple Wiener-It\^o integrals
Peccati, Giovanni UL; Taqqu, Murad S.

in Journal of Theoretical Probability (2008), 21(3), 527--570

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