N. V. Krylov
We present several results on smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form filtering equation which are usually considered in terms of formally adjoint to operators in nondivergence form.
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
We present several results on the smoothness in $L_{p}$ sense of filtering densities under the Lipschitz continuity assumption on the coefficients of a partially observable diffusion processes. We obtain them by rewriting in divergence form filtering equation which are usually considered in terms of formally adjoint to operators in nondivergence form.
This paper is the first part of a series of papers on filtering for partially observed jump diffusions satisfying a stochastic differential equation driven by Wiener processes and Poisson martingale measures. The coefficients of the equation only satisfy appropriate growth conditions. Some results in filtering theory of diffusion processes are extended to jump diffusions and equations for the time evolution of the conditional distribution and the unnormalised conditional distribution of the unobserved process at time $t$, given the observations until $t$, are presented.
We prove that under Hörmander's type conditions on the coefficients of the unobservable component of a partially observable diffusion process the filtering density is infinitely differentiable and can be represented as the integral of an infinitely differentiable kernel against the prior initial distribution. These results are derived from more general results obtained for SPDEs. One the main novelty of the paper is the existence and smoothness of the kernel, another that we allow the coefficients of our partially observable process to be just measurable with respect to the time variable.
The filtering equations associated to a partially observed jump diffusion model $(Z_t)_{t\in [0,T]}=(X_t,Y_t)_{t\in [0,T]}$, driven by Wiener processes and Poisson martingale measures are considered. Building on results from two preceding articles on the filtering equations, the regularity of the conditional density of the signal $X_t$, given observations $(Y_s)_{s\in [0,t]}$, is investigated, when the conditional density of $X_0$ given $Y_0$ exists and belongs to a Sobolev space, and the coefficients satisfy appropriate smoothness and growth conditions.
Particle filtering methods for partially observed branching processes
本文研究了部分观测分支过程的参数估计问题，提出基于序列蒙特卡洛方法的计算工具进行贝叶斯推断，并应用Liu-West粒子滤波器对流行病模型进行参数估计。
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $ν$ whose components have paths of bounded variation. The presence of the process $ν$ prevents from directly applying classical results and novel estimates need to be derived. By making use of the so-called reference probability measure approach, we derive the Zakai equation satisfied by the unnormalized filtering process, and then we deduce the corresponding Kushner-Stratonovich equation. Under the condition that the jump times of the process $ν$ do not accumulat…
We derive the forward and backward filtering equations for a class of degenerate partially observable diffusions, satisfying the weak Hörmander condition. Our approach is based on the Hölder theory for degenerate SPDEs that allows to pursue the direct approaches proposed by N. V. Krylov and A. Zatezalo, and A. Yu. Veretennikov, avoiding the use of general results from filtering theory. As a by-product we also provide existence, regularity and estimates for the filtering density.
The connection between forward backward doubly stochastic differential equations and the optimal filtering problem is established without using the Zakai's equation. The solutions of forward backward doubly stochastic differential equations are expressed in terms of conditional law of a partially observed Markov diffusion process. It then follows that the adjoint time-inverse forward backward doubly stochastic differential equations governs the evolution of the unnormalized filtering density in the optimal filtering problem.
Optimal linear filtering of partially observed polynomial processes in discrete and continuous time
针对部分观测的多项式过程，利用其与高斯过程在二阶矩上的不可区分性，构造高斯等价过程并显式计算最优线性滤波器、预测器和平滑器。
On partially observed jump diffusions II. The filtering density
本文研究由维纳过程和泊松鞅测度驱动的部分观测跳扩散过程，在系数满足利普希茨与增长条件下，证明了初始条件密度的$L_p$存在性可推出任意时刻滤波密度的$L_p$存在性。
The objective of this paper is to study the filtering problem for a system of partially observable processes $(X, Y)$, where $X$ is a non-Markovian pure-jump process representing the signal and $Y$ is a general jump-diffusion which provides observations. Our model covers the case where both processes are not necessarily quasi left-continuous, allowing them to jump at predictable stopping times. By introducing the Markovian version of the signal, we are able to compute an explicit equation for the filtering process via the innovations approach.
Stochastic Filtering of Reaction Networks Partially Observed in Time Snapshots
针对时间快照部分观测下随机反应网络的条件概率分布估计问题，提出一种利用非齐次泊松过程进行精确插值的targeting method粒子滤波方法，并提供了严格分析与数值验证。
In traditional work on numerical schemes for solving stochastic differential equations (SDEs), it is usually assumed that the coefficients are globally Lipschitz. This assumption has been used to establish a powerful analysis of the numerical approximations of the solutions of stochastic differential equations. In practice, however, the globally Lipschitz assumption on the coefficients is on occasion too stringent a requirement to meet. Some Brownian motion driven SDEs used in applications have coefficients that are Lipschitz only on compact sets. Reflecting the importance of the locally Lipsc…
We obtain sharp gradient bounds for perturbed diffusion semigroups. In contrast with existing results, the perturbation is here random and the bounds obtained are pathwise. Our approach builds on the classical work of Kusuoka and Stroock [7],[9],[10],[11], and extends their program developed for the heat semi-group to solutions of stochastic partial differential equations. The work is motivated by and applied to nonlinear filtering. The analysis allows us to derive pathwise gradient bounds for the un-normalised conditional distribution of a partially observed signal. It uses a pathwise represe…
This paper is concerned with the nonlinear filtering problem for a general Markovian partially observed system (X,Y), whose dynamics is modeled by correlated jump-diffusions having common jump times. At any time t, the sigma-algebra generated by the observation process Y provides all the available information about the signal X. The central goal of stochastic filtering is to characterize the filter which is the conditional distribution of X, given the observed data. It has been proved in Ceci-Colaneri (2012) that the filter is the unique probability measure-valued process satisfying a nonlinea…
We study a stochastic optimal control problem for a partially observed diffusion. By using the control randomization method in [4], we prove a corresponding randomized dynamic programming principle (DPP) for the value function, which is obtained from a flow property of an associated filter process. This DPP is the key step towards our main result: a characterization of the value function of the partial observation control problem as the unique viscosity solution to the corresponding dynamic programming Hamilton-Jacobi-Bellman (HJB) equation. The latter is formulated as a new, fully non linear …
By using the fact that the space of all probability measures with finite support can be somehow completed in two different fashions, one generating the Arens-Eells space and another generating the Kantorovich-Wasserstein (Wasserstein-1) space, and by exploiting the duality relationship between the Arens-Eells space with the space of Lipschitz functions, we provide a dual representation of Fenchel-Moreau-Rockafellar type for proper convex functionals on Wasserstein-1. We retrieve dual transportation inequalities as a Corollary and we provide examples where the theorem can be used to easily prov…
We prove Hörmander's type hypoellipticity theorem for stochastic partial differential equations when the coefficients are only measurable with respect to the time variable. The need for such kind of results comes from filtering theory of partially observable diffusion processes, when even if the initial system is autonomous, the observation process enters the coefficients of the filtering equation and makes them time-dependent with no good control on the smoothness of the coefficients with respect to the time variable.
Numerical approximations of stochastic differential equations with non-globally Lipschitz continuous coefficients
针对漂移或扩散系数超线性增长的随机微分方程，基于稀有事件理论建立离散时间随机过程的矩界，证明全隐式、部分隐式及一类新显式方法的矩有界性和强收敛性。
We consider a continuous-time model for inventory management with Markov modulated non-stationary demands. We introduce active learning by assuming that the state of the world is unobserved and must be inferred by the manager. We also assume that demands are observed only when they are completely met. We first derive the explicit filtering equations and pass to an equivalent fully observed impulse control problem in terms of the sufficient statistics, the a posteriori probability process and the current inventory level. We then solve this equivalent formulation and directly characterize an opt…
Deep ZakaiJ: Structured Filtering for Jump-Diffusion Time Series Forecasting
提出Deep ZakaiJ模型，将Zakai非线性滤波方程嵌入神经编码器-解码器架构，通过Strang分裂实现隐状态信念更新，用于部分观测的跳跃扩散系统，在合成、金融和海洋数据集上改进了分布预测并保持点精度竞争力。
Gaussian approximations for fast Bayesian inference of partially observed branching processes with applications to epidemiology
本文提出基于高斯近似的快速贝叶斯推断方法，用于部分观测分支过程，应用于流行病学模型和新冠数据集，实现高效推断和计算加速。
Strong and weak quantitative estimates in slow-fast diffusions using filtering techniques
本文用非线性滤波和Kushner-Stratonovich方程，重新证明慢快扩散的强（$n^{-1/2}$）与弱（$n^{-1}$）最优收敛速率，核心是加权Lipschitz距离估计。
Transformers Can Solve Non-Linear and Non-Markovian Filtering Problems in Continuous Time For Conditionally Gaussian Signals
本文提出filterformers模型，通过自定义注意力机制近似实现非马尔可夫且条件高斯信号过程的条件分布，解决了随机过滤问题的理论基础。
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。