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Consider the problem of learning the drift coefficient of a stochastic differential equation from a sample path. In this paper, we assume that the drift is parametrized by a highdimensional vector. We...
We develop computational bounds on performance for causal state feedback stochastic control with linear dynamics, arbitrary noise distribution, and arbitrary input constraint set. This can be very use...
For infinitely divisible distributions  on Rd the stochastic integral map-ping f  is defined as the distribution of improper stochastic integral R∞−0 f(s)dX() s ,where f(s) is a non-random f...
We construct normed spaces of real-valued functions with controlled growth on possibly infinite-dimensional state spaces such that semigroups of positive, bounded operators $(P_t)_{t\ge 0}$ thereon w...
By using a simple observation that the density processes appearing in Ito's martingale representation theorem are invariant under the change of measures, we establish a non-linear version of the Came...
In this note, we study one-dimensional reflected backward doubly stochastic differential equations (RBDSDEs) with one continuous barrier and discontinuous generator (left-or right-continuous). By a c...
A new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with L\'evy process are investigated. We establish a compariso...
We prove an existence and uniqueness result for the infinitely delayed stochastic evolution equation $$dU(t) = &\big(AU(t) + F(t,U_t)\big) dt + B(t,U_t)dW_H(t), t\in[0,T_0]$$ where $A$ is the generat...
In this paper, a class of generalized backward doubly stochastic differential equations whose coefficient contains the subdifferential operators of two convex functions (also called generalized backw...
In this paper, we deal with a class of backward doubly stochastic differential equations (BDSDEs, in short) involving subdifferential operator of a convex function and driven by Teugels martingales a...
It is well-known that solutions of backward differential equations are continuously dependent on the terminal value. Since the increasing part of the minimal solution of a constrained backward differe...
The goal of this paper is to solve backward doubly stochastic differential equation (BDSDE, in short) under weak assumptions on the data. The first part is devoted to the development of some new techn...
We consider a lattice gas on the discrete d-dimensional torus (Z/NZ)^d with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas perf...
We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential ...
We first prove some general results on pathwise uniqueness,comparison property and existence of non-negative strong solutions of stochastic equations driven by white noises and Poisson random measures...

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