相关论文: Ergodic BSDEs with Multiplicative and Degenerate N…

In an incomplete market, with incompleteness stemming from stochastic factors imperfectly correlated with the underlying stocks, we derive representations of homothetic (power, exponential and logarithmic) forward performance processes in…

This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant…

We study existence and uniqueness of the invariant measure for a stochastic process with degenerate diffusion, whose infinitesimal generator is a linear subelliptic operator in the whole space R N with coefficients that may be unbounded.…

Inverse problems in scientific computing often require optimization over infinite-dimensional Hilbert spaces. A commonly used solver in such settings is stochastic gradient descent (SGD), where gradients are approximated using randomly…

In this paper we study the finite-horizon optimal covariance steering problem for a continuous-time linear stochastic system subject to both additive and multiplicative noise. The noise can be continuous or it may contain jumps. Additive…

Diffusion with stochastic transport is investigated here when the random driving process is a very general Gaussian process, including Fractional Brownian motion. The purpose is the comparison with a deterministic PDE, which in certain…

We address a general optimal switching problem over finite horizon for a stochastic system described by a differential equation driven by Brownian motion. The main novelty is the fact that we allow for infinitely many modes (or regimes,…

Motivated by a problem of optimal harvesting of natural resources, we study a control problem for Volterra type dynamics driven by time-changed L\'evy noises, which are in general not Markovian. To exploit the nature of the noise, we make…

We study a new class of ergodic backward stochastic differential equations (EBSDEs for short) which is linked with semi-linear Neumann type boundary value problems related to ergodic phenomenas. The particularity of these problems is that…

In this paper, we study a class of Anticipated Backward Stochastic Differential Equations (ABSDE) with jumps. The solution of the ABSDE is a triple $(Y,Z,\psi)$ where $Y$ is a semimartingale, and $(Z,\psi)$ are the diffusion and jump…

We consider an infinite horizon, obliquely reflected backward stochastic differential equation (RBSDE). The main contribution of the present work is that we generalize previous results on infinite horizon reflected BSDEs to the setting…

In this article, we deal with a multiple dimensional coupled Markovian BSDEs system with stochastic linear growth generators with respect to volatility processes. An existence result is provided by using approximation techniques.

We address a class of backward stochastic differential equations on a bounded interval, where the driving noise is a marked, or multivariate, point process. Assuming that the jump times are totally inaccessible and a technical condition…

In this paper, we discuss the solvability of backward stochastic differential equations (BSDEs) with superquadratic generators. We first prove that given a superquadratic generator, there exists a bounded terminal value, such that the…

Exponentiated gradient descent (EGD), a biologically motivated optimisation algorithm that respects Dale's law, produces log-normally distributed synaptic weights at convergence, in alignment with experimental observations in neuroscience.…

In this paper we study, by probabilistic techniques, the convergence of the value function for a two-scale, infinite-dimensional, stochastic controlled system as the ratio between the two evolution speeds diverges. The value function is…

Using small noise limit approach, we study degenerate stochastic ergodic control problems and as a byproduct obtain error bounds for the $\varepsilon$-optimal controls. We also establish tunneling for a special ergodic control problem and…

We establish general quantitative conditions for stochastic evolution equations with locally monotone drift and degenerate additive Wiener noise in variational formulation resulting in the existence of a unique invariant probability measure…

A stochastic variational inequality is proposed to model an elasto-plastic oscillator excited by a filtered white noise. We prove the ergodic properties of the process and characterize the corresponding invariant measure. This extends…

In this paper, we establish the ergodicity for stochastic 2D Navier-Stokes equations driven by a highly degenerate pure jump L\'evy noise. The noise could appear in as few as four directions. This gives an affirmative anwser to a…