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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...
In this article, we address the dynamics and bifurcations of a wide class of stochastic differential equations around singular points where both the drift and diffusion functions vanish. We apply thes...
The existence and uniqueness for solution of backward doubly stochastic differential equations with Brownian motions and Poisson process and that of forward-backward doubly stochastic differential equ...
A type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. Under some natural monotonicity assumptions, the existence and uniqueness result is established.
Exploring functional analysis methods, this paper gives an existence theorem of strong solutions for a class of backward stochastic differential equations(BSDEs) with left-Lipschitz coefficients (may ...
Abstract: In this paper we consider stochastic differential equations with non-negativity constraints, driven by a fractional Brownian motion with Hurst parameter $H>\1/2$. We first study an ordinary ...
Abstract: We introduce and develop a pathwise description of the dissipation of general convex entropies for continuous time Markov processes, based on simple backward martingales and convergence theo...
Abstract: This paper extends the idea of E.Gobet, J.P.Lemor and X.Warin from the setting of Backward Stochastic Differential Equations to that of Backward Doubly Stochastic Differential equations. We ...
We consider the problem of valuation of American (call and put) options written on a dividend paying stock governed by the geometric Brownian motion. We show that the value function has two different ...
The filtering problem have an important role in the theory of stochastic differential equations(SDEs). In this paper, we present an application of the continuous Kalman-Bucy filter for a RC circuit. T...
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...
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...

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