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Unique Ergodicity for Fractionally Dissipated, Stochastically Forced 2D Euler Equations
Unique Ergodicity Fractionally Dissipated Stochastically Forced 2D Euler Equations
2014/4/3
We establish the existence and uniqueness of an ergodic invariant measure for 2D fractionally dissipated stochastic Euler equations on the periodic box, for any power of the dissipation term.
A STOCHASTIC-LAGRANGIAN APPROACH TO THE NAVIER-STOKES EQUATIONS IN DOMAINS WITH BOUNDARY.
The (unforced) incompressible Navier-Stokes equations STOCHASTIC-LAGRANGIAN
2014/4/3
In this paper we derive a probabilistic representation of the deterministic 3-dimensional Navier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial bound...
Gradient estimates for porous medium and fast diffusion equations via FBSDE approach
Gradient estimates porous medium fast diffusion equations FBSDE approach Probability
2012/6/27
In this paper, we establish several gradient estimates for the positive solution of Porous Medium Equations (PMEs) and Fast Diffusion Equations (FDEs). Our proof is probabilistic and uses martingale t...
Strictly stationary solutions of ARMA equations in Banach spaces
Strictly stationary solutions ARMA equations Banach spaces Probability
2012/6/21
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain ass...
Bifurcations of stochastic differential equations with singular diffusion coefficients
bifurcations noise universal unfolding stochastic stability (quasi)-stationary distributions normal forms
2012/5/9
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...
Forward-Backward Doubly Stochastic Differential Equations with Brownian Motions and Poisson Process
Forward-backward doubly stochastic differential equations stochastic analysis random measure Poisson process
2011/11/7
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...
FORWARD-BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS
Forward-backward doubly stochastic differential equations equivalent norm, contraction mapping
2011/11/7
A type of forward-backward doubly stochastic differential equations (FBDSDEs) is studied. Under some natural monotonicity assumptions, the existence and uniqueness result is established.
Backward Stochastic Differential Equations with Discontinuous Coefficients
Backward stochastic differential equation discontinuous generator strong solution weak solution
2011/11/5
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 ...
Stability of nonlinear stochastic Volterra difference equations with continuous time
Nonlinear stochastic difference equations Stability Lyapunov functional construction Continuous time
2011/11/4
In recent years, many authors investigated the systems of stochastic difference equations with discrete time or the systems of numerical solution for stochastic difference equations with continue time...
Stochastic differential equations with non-negativity constraints driven by fractional Brownian motion with Hurst parameter H $>$ 1/2
stochastic differential equations normal reflection fractional Brownian motion Young integral
2011/9/22
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 ...
A trajectorial interpretation of the dissipations of entropy and Fisher information for stochastic differential equations
entropy and Fisher information stochastic differential equations Probability
2011/9/13
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...
Rare event simulation for processes generated via stochastic fixed point equations
Monte Carlo methods importance sampling perpetuities large deviations nonlinear renewal theory Harris recurrent Markov chains
2011/9/13
Abstract: In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable V satisfying the distributional...
Fractional relaxation equations and Brownian crossing probabilities of a random boundary
Fractional relaxation equation Generalized Mittag-Leffler functions Processes with random time
2011/9/5
Abstract: We analyze here different forms of fractional relaxation equations of order {\nu}\in(0,1) and we derive their solutions both in analytical and in probabilistic forms. In particular we show t...
A regression Monte-Carlo method for Backward Doubly Stochastic Differential Equations
regression Monte-Carlo method Stochastic Differential Equations Probability
2011/8/30
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 ...
Markov processes and generalized Schroedinger equations
Markov processes Stochastic mechanics Doob transformation
2011/8/26
Abstract: Starting from the forward and backward infinitesimal generators of bilateral, time-homogeneous Markov processes, the self-adjoint Hamiltonians of the generalized Schroedinger equations are f...