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Functional inequalities for Feynman-Kac semigroups Thompson, James 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 ▲] Detailed reference viewed: 113 (28 UL)On the favorite points of symmetric Lévy processes. ; ; Yang, Xiaochuan in Journal of Theoretical Probability (2019) Detailed reference viewed: 62 (1 UL)Derivatives of Feynman-Kac Semigroups Thompson, James 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 ▲] Detailed reference viewed: 173 (55 UL)Hausdorff dimension of the range and the graph of stable-like processes Yang, Xiaochuan in Journal of Theoretical Probability (2018) Detailed reference viewed: 51 (2 UL)Reflecting diffusion semigroup on manifolds carrying geometric flow Cheng, Li Juan ; 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 ▲] Detailed reference viewed: 145 (32 UL)Classical and free fourth moment theorems: universality and thresholds Nourdin, Ivan ; Peccati, Giovanni ; et al in Journal of Theoretical Probability (2016), 29(2), 653-680 Detailed reference viewed: 131 (8 UL)Martingales on manifolds with time-dependent connection Guo, Hongxin ; Philipowski, Robert ; Thalmaier, Anton 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 ▲] Detailed reference viewed: 314 (46 UL)Distributional transformations without orthogonality relations Döbler, Christian in Journal of Theoretical Probability (2015) Detailed reference viewed: 136 (6 UL)Central and non-central limit theorems in a free probability setting Nourdin, Ivan ; in Journal of Theoretical Probability (2014), 27(1), 220-248 Detailed reference viewed: 73 (2 UL)A quantitative central limit theorem for linear statistics of random matrix eigenvalues Döbler, Christian ; in Journal of Theoretical Probability (2014) Detailed reference viewed: 61 (1 UL)Rate of Convergence for Discretization of Integrals with Respect to Fractional Brownian Motion Azmoodeh, Ehsan ; 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 ▲] Detailed reference viewed: 79 (2 UL)Asymptotic theory for fractional regression models via Malliavin calculus Bourguin, Solesne ; in Journal of Theoretical Probability (2012), 25(2), 536-564 Detailed reference viewed: 47 (1 UL)Central limit theorems for multiple Skorohod integrals Nourdin, Ivan ; in Journal of Theoretical Probability (2010), 23(1), 39-64 Detailed reference viewed: 26 (4 UL)Stable convergence of multiple Wiener-It\^o integrals Peccati, Giovanni ; in Journal of Theoretical Probability (2008), 21(3), 527--570 Detailed reference viewed: 126 (0 UL)Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion ; Nourdin, Ivan in Journal of Theoretical Probability (2008), 20(4), 871-899 Detailed reference viewed: 66 (6 UL) |
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