Dejun Luo
We consider the Fokker-Planck equation on the abstract Wiener space associated to the Ornstein-Uhlenbeck operator. Using the Weitzenböck formula, we prove an explicit estimate on the time derivative of the entropy of the solution to the Fokker-Planck equation.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Entropy of Wiener integrals with respect to fractional Brownian motion
本文详细研究了指数-Wiener积分分数高斯过程（EWIFG过程）的熵的单调性性质，指出其熵行为比分数布朗运动更复杂且依赖于时间矩。
We propose a set-indexed family of capacities $\{\cap_G \}_{G \subseteq \R_+}$ on the classical Wiener space $C(\R_+)$. This family interpolates between the Wiener measure ($\cap_{\{0\}}$) on $C(\R_+)$ and the standard capacity ($\cap_{\R_+}$) on Wiener space. We then apply our capacities to characterize all quasi-sure lower functions in $C(\R_+)$. In order to do this we derive the following capacity estimate which may be of independent interest: There exists a constant $a > 1$ such that for all $r > 0$, \[ \frac {1}{a} \K_G(r^6) e^{-π^2/(8r^2)} \le \cap_G \{f^* \le r\} \le a \K_G(r^6) e^{-π^2…
Let $(W,H,μ)$ be the classical Wiener space where $H$ is the Cameron-Martin space which consists of the primitives of the elements of $L^2([0,1],\,dt)\otimes \R^d$, we denote by $L^2_a(μ,H)$ the equivalence classes w.r.t. $dt\times dμ$ whose Lebesgue densities $s\to\dot{u}(s,w)$ are almost surely adapted to the canonical Brownian filtration. If $f$ is a Wiener functional s.t. $\frac{1}{E[e^{-f}]}e^{-f}dμ$ is of finite relative entropy w.r.t. $μ$, we prove that \beaa J_\star&=& \inf\left(E_μ\left[f\circ U+\half |u|_H^2\right]: u\in L_a^2(μ,H)\right)\\ &\geq&-\log E_μ[e^{-f}]=\inf\left(\int_W fd…
Generalized specific entropy on Wiener space with application to Martingale Optimal Transport
本文提出了一种基于泊松跳跃近似的特定熵框架，用于连续时间鞅传输问题，解决了传统熵正则化在连续时间中的局限性，并引入了广义特定熵函数在维纳空间上的显式表达，提出了连续时间特定熵鞅最优传输问题SEMOT。
We provide a framework to derive a variational formulation for $-\log\mathbb{E}_ν\left[e^{-f}\right]$ for a large class of measures $ν$. We use a family of perturbations of the identity $(W^u)$ whose invertibility we characterize thanks to entropy. This yields results of strong existence for various stochastic differential equations. We also discuss the attainability of the infimum in the variational formulation and we derive a Prékopa-Leindler theorem for the measure $ν$.
In this work we study the necessary and sufficient conditions for a positive random variable whose expectation under the Wiener measure is one, to be represented as the Radon-Nikodym derivative of the image of the Wiener measure under an adapted perturbation of identity with the help of the associated innovation process. We prove that the innovation conjecture holds if and only if the original process is almost surely invertible. We also give variational characterizations of the invertibility of the perturbations of identity and the representability of a positive random variable whose total ma…
In this paper we study two basic facts of optimal transportation on Wiener space W. Our first aim is to answer to the Monge Problem on the Wiener space endowed with the Sobolev type norm (k,gamma) to the power of p (cases p = 1 and p > 1 are considered apart). The second one is to prove 1-convexity (resp. C-convexity) along (constant speed) geodesics of relative entropy in (P2(W);W2), where W is endowed with the infinite norm (resp. with (k,gamma) norm), and W2 is the 2-distance of Wasserstein.
Let $(W,H,μ)$ be the classical Wiener space, assume that $U=I_W+u$ is an adapted perturbation of identity satisfying the Girsanov identity. Then, $U$ is invertible if and only if the kinetic energy of $u$ is equal to the relative entropy of the measure induced with the action of $U$ on the Wiener measure $μ$, in other words $U$ is invertible if and only if $$ \half \int_W|u|_H^2dμ=\int_W \frac{dUμ}{dμ}\log\frac{dUμ}{dμ}dμ. $$
A criterion for proving entropy chaos on path space
本文提出了一种在路径空间上证明强形式熵混沌的判据，针对一类保守扩散过程，证明在粒子数趋于无穷时，满足特定正则性条件的极限漂移可实现强熵混沌。
Let $(W,H,μ)$ be the classical Wiener space, assume that $U_\la=I_W+u_\la$ is an adapted perturbation of identity where the perturbation $u_\la$ is an $H$-valued map, defined up to $μ$-equivalence classes, such that its Lebesgue density $s\to \dot{u}_\la(s)$ is almost surely adapted to the canonical filtration of the Wiener space and depending measurably on a real parameter $\la$. Assuming some regularity for $u_\la$, its Sobolev derivative and integrability of the divergence of the resolvent operator of its Sobolev derivative, we prove the almost sure and $L^p$-regularity w.r. to $\la$ of the…
We develop a technique based on Malliavin-Bismut calculus ideas, for asymptotic expansion of dual control problems arising in connection with exponential indifference valuation of claims, and with minimisation of relative entropy, in incomplete markets. The problems involve optimisation of a functional of Brownian paths on Wiener space, with the paths perturbed by a drift involving the control. In addition there is a penalty term in which the control features quadratically. The drift perturbation is interpreted as a measure change using the Girsanov theorem, leading to a form of the integratio…
Minimum Relative Entropy State Transitions in Linear Stochastic Systems: the Continuous Time Case
针对具有不确定漂移的线性伊藤随机微分方程驱动的动态系统，基于相对熵耗散不等式，通过非线性代数技术求解哈密顿-雅可比方程，得到给定高斯状态分布间最小相对熵供给的闭式光滑解。
Uniform Partition-Function Estimates for Coulomb Modulated Energy at All Positive Temperatures
该研究证明了所有正温度下三类核的中心调制能量的均匀配分函数估计，应用该估计得到了吉布斯测度的相关熵界、平均场收敛等结果，还确定了配分函数拉普拉斯变换的行列式表示及参数行为。
Renyi's Relative Entropy Lyapunov Functional for Convergence to Invariant Measure in Dissipative Stochastic Hamiltonian Systems
本文针对耗散随机哈密顿系统，证明χ²散度（Renyi二阶相对熵）作为Lyapunov泛函，通过位置-动量条件化确保其严格递减，从而保证系统收敛到Boltzmann不变测度。
On the Equivalence of Stochastic Control and Path Space Formulations for Schrödinger Bridges over Compact Connected Lie Groups
本文证明紧连通李群上薛定谔桥问题的随机控制与路径空间表述等价，并给出分析、概率和计算三方面意义，数值验证于环面。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。