30 citations · 119 across the 28 of their papers we have counts for
19 papers · 1 filter
Quantitative weak propagation of chaos for McKean--Vlasov branching diffusion processes
Wenjing Cao, Zhenjie Ren, Xiaolu Tan
We study in this paper the weak propagation of chaos for McKean--Vlasov diffusions with branching, whose induced marginal measures are nonnegative finite measures but not necessary…
Uniform-in-time propagation of chaos for kinetic mean field Langevin dynamics
Fan Chen, Yiqing Lin, Zhenjie Ren +1
We study the kinetic mean field Langevin dynamics under the functional convexity assumption of the mean field energy functional. Using hypocoercivity, we first establish the expone…
Mean Field Optimization Problem Regularized by Fisher Information
Julien Claisse, Giovanni Conforti, Zhenjie Ren +1
Recently there is a rising interest in the research of mean field optimization, in particular because of its role in analyzing the training of neural networks. In this paper by add…
Uniform-in-time propagation of chaos for mean field Langevin dynamics
Fan Chen, Zhenjie Ren, Songbo Wang
We study the mean field Langevin dynamics and the associated particle system. By assuming the functional convexity of the energy, we obtain the -convergence of the marginal di…
On path-dependent multidimensional forward-backward SDEs
Kaitong Hu, Zhenjie Ren, Nizar Touzi
This paper extends the results of Ma, Wu, Zhang, Zhang [11] to the context of path-dependent multidimensional forward-backward stochastic differential equations (FBSDE). By path-de…
Entropic turnpike estimates for the kinetic Schrödinger problem
Alberto Chiarini, Giovanni Conforti, Giacomo Greco +1
We investigate the kinetic Schrödinger problem, obtained considering Langevin dynamics instead of Brownian motion in Schrödinger's thought experiment. Under a quasilinearity assump…
Ergodicity of the underdamped mean-field Langevin dynamics
Anna Kazeykina, Zhenjie Ren, Xiaolu Tan +1
We study the long time behavior of an underdamped mean-field Langevin (MFL) equation, and provide a general convergence as well as an exponential convergence rate result under diff…
Continuous-Time Principal-Agent Problem in Degenerate Systems
Kaitong Hu, Zhenjie Ren, Nizar Touzi
In this paper we present a variational calculus approach to Principal-Agent problem with a lump-sum payment on finite horizon in degenerate stochastic systems, such as filtered par…
Mean-field Langevin System, Optimal Control and Deep Neural Networks
Kaitong Hu, Anna Kazeykina, Zhenjie Ren
In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introd…
Mean-Field Langevin Dynamics and Energy Landscape of Neural Networks
Kaitong Hu, Zhenjie Ren, David Siska +1
Our work is motivated by a desire to study the theoretical underpinning for the convergence of stochastic gradient type algorithms widely used for non-convex learning tasks such as…
Principal-agent problem with multiple principals
Kaitong Hu, Zhenjie Ren, Junjian Yang
We consider a moral hazard problem with multiple principals in a continuous-time model. The agent can only work exclusively for one principal at a given time, so faces an optimal s…
Nonlinear predictable representation and -solutions of backward SDEs and second-order backward SDEs
Zhenjie Ren, Nizar Touzi, Junjian Yang
The theory of backward SDEs extends the predictable representation property of Brownian motion to the nonlinear framework, thus providing a path-dependent analog of fully nonlinear…
Viscosity solutions of path-dependent PDEs with randomized time
Zhenjie Ren, Mauro Rosestolato
We introduce a new definition of viscosity solution to path-dependent partial differential equations, which is a slight modification of the definition introduced in [8]. With the n…
Second order backward SDE with random terminal time
Yiqing Lin, Zhenjie Ren, Nizar Touzi +1
Backward stochastic differential equations extend the martingale representation theorem to the nonlinear setting. This can be seen as path-dependent counterpart of the extension fr…
A dual algorithm for stochastic control problems: Applications to Uncertain Volatility Models and CVA
Pierre Henry-Labordère, Christian Litterer, Zhenjie Ren
We derive an algorithm in the spirit of Rogers and Davis & Burstein that leads to upper bounds for stochastic control problems. Our bounds complement lower biased estimates recentl…
On the convergence of monotone schemes for path-dependent PDE
Zhenjie Ren, Xiaolu Tan
We propose a reformulation of the convergence theorem of monotone numerical schemes introduced by Zhang and Zhuo for viscosity solutions of path-dependent PDEs, which extends the s…
Perron's method for viscosity solutions of semilinear path dependent PDEs
Zhenjie Ren
This paper proves the existence of viscosity solutions of path dependent semilinear PDEs via Perron's method, i.e. via showing that the supremum of viscosity subsolutions is a visc…
Comparison of Viscosity Solutions of Semi-linear Path-Dependent PDEs
Zhenjie Ren, Nizar Touzi, Jianfeng Zhang
This paper provides a probabilistic proof of the comparison result for viscosity solutions of path-dependent semilinear PDEs. We consider the notion of viscosity solutions introduc…
Large Deviations for Non-Markovian Diffusions and a Path-Dependent Eikonal Equation
Jin Ma, Zhenjie Ren, Nizar Touzi +1
This paper provides a large deviation principle for Non-Markovian, Brownian motion driven stochastic differential equations with random coefficients. Similar to Gao and Liu \cite{G…