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Information Theoretic Limits on Learning Stochastic Differential Equations
Stochastic differential equation the coefficient
2015/8/21
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...
A condition on delay for differential equations with discrete state-dependent delay
differential equations discrete state-dependent delay
2010/11/23
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equ...
Loewner Theory in annulus I: evolution families and differential equations
Loewner Theory differential equations
2010/11/23
Loewner Theory, based on dynamical viewpoint, is a powerful tool in Complex Analysis, which plays a crucial role in such important achievements as the proof of famous Bieberbach's conjecture and well...
A Semigroup Point Of View On Splitting Schemes For Stochastic (Partial) Differential Equations
Semigroup Point Splitting Schemes Differential Equations
2010/11/18
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...
On Girsanov's transform for backward stochastic differential equations
stochastic differential equations math
2010/11/19
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...
Reflected backward doubly stochastic differential equations with discontinuous generator
stochastic differential equations discontinuous generator
2010/11/19
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...
Generalized backward doubly stochastic differential equations driven by Lévy processes with continuous coefficients
stochastic differential equations continuous coefficients
2010/11/19
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...
Multivalued stochastic Dirichlet-Neumann problems and generalized backward doubly stochastic differential equations
Dirichlet-Neumann problems stochastic differential equations
2010/11/19
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...
Multivalued stochastic partial differential-integral equations via backward doubly stochastic differential equations driven by a Lévy process
partial differential-integral equations stochastic differential equations
2010/11/19
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...
On the continuous dependence of the minimal solution of constrained backward stochastic differential equations
the minimal solution stochastic differential equations
2010/11/15
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...
L^{p}-solutions of backward doubly stochastic differential equations
stochastic differential equations math
2010/11/19
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...
Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains
Spatial Besov Regularity Partial Differential Equations Lipschitz Domains
2010/11/15
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 ...
Preconditioners based on Windowed Fourier Frames Applied to Elliptic Partial Differential Equations
Windowed Fourier frame symbol elliptic PDE preconditioner
2010/12/3
We investigate the application of windowed Fourier frames (WFFs) to the numerical solution of partial di erential equations, focussing on elliptic equations. The action of a partial di erential operat...
Exponential decay of semigroups for second order non-selfadjoint linear differential equations
Accretive operator sectorial operator C0-semigroup
2011/1/20
The Cauchy problem for second order linear differential equation u′′(t) + Du′(t) + Au(t) = 0
in Hilbert space H with a sectorial operator A and an accretive operator D is studied. Sufficient conditio...
More common errors in finding exact solutions of nonlinear differential equations. I
nonlinear differential equations common errors
2010/4/7
In the recent paper by Kudryashov [Commun. Nonlinear Sci. Numer. Simulat., 2009, V.14, 3507-3529] seven common errors in finding exact solutions of nonlinear differential equations were listed and dis...